WorldWideScience

Sample records for closed timelike geodesics

  1. Timelike geodesics around a charged spherically symmetric dilaton black hole

    Directory of Open Access Journals (Sweden)

    Blaga C.

    2015-01-01

    Full Text Available In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.

  2. Generating geodesic flows and supergravity solutions

    NARCIS (Netherlands)

    Bergshoeff, E.; Chemissany, W.; Ploegh, A.; Trigiante, M.; Van Riet, T.

    2009-01-01

    We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacellike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike p-brane Solutions when they are lifted over a p-dimensional flat space. In particular, we consider

  3. Exact geodesic distances in FLRW spacetimes

    Science.gov (United States)

    Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

    2017-11-01

    Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

  4. Experimental simulation of closed timelike curves.

    Science.gov (United States)

    Ringbauer, Martin; Broome, Matthew A; Myers, Casey R; White, Andrew G; Ralph, Timothy C

    2014-06-19

    Closed timelike curves are among the most controversial features of modern physics. As legitimate solutions to Einstein's field equations, they allow for time travel, which instinctively seems paradoxical. However, in the quantum regime these paradoxes can be resolved, leaving closed timelike curves consistent with relativity. The study of these systems therefore provides valuable insight into nonlinearities and the emergence of causal structures in quantum mechanics--essential for any formulation of a quantum theory of gravity. Here we experimentally simulate the nonlinear behaviour of a qubit interacting unitarily with an older version of itself, addressing some of the fascinating effects that arise in systems traversing a closed timelike curve. These include perfect discrimination of non-orthogonal states and, most intriguingly, the ability to distinguish nominally equivalent ways of preparing pure quantum states. Finally, we examine the dependence of these effects on the initial qubit state, the form of the unitary interaction and the influence of decoherence.

  5. Geodesic stability, Lyapunov exponents, and quasinormal modes

    International Nuclear Information System (INIS)

    Cardoso, Vitor; Miranda, Alex S.; Berti, Emanuele; Witek, Helvi; Zanchin, Vilson T.

    2009-01-01

    Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d≥6.

  6. Supertube domain walls and elimination of closed timelike curves in string theory

    International Nuclear Information System (INIS)

    Drukker, Nadav

    2004-01-01

    We show that some novel physics of supertubes removes closed timelike curves from many supersymmetric spaces which naively suffer from this problem. The main claim is that supertubes naturally form domain walls, so while analytical continuation of the metric would lead to closed timelike curves, across the domain wall the metric is nondifferentiable, and the closed timelike curves are eliminated. In the examples we study, the metric inside the domain wall is always of the Goedel type, while outside the shell it looks like a localized rotating object, often a rotating black hole. Thus this mechanism prevents the appearance of closed timelike curves behind the horizons of certain rotating black holes

  7. Transversal Surfaces of Timelike Ruled Surfaces in Minkowski 3-Space

    OpenAIRE

    Önder, Mehmet

    2012-01-01

    In this study we give definitions and characterizations of transversal surfaces of timelike ruled surfaces. We study some special cases such as the striction curve is a geodesic, an asymptotic line or a line of curvature. Moreover, we obtain developable conditions for transversal surfaces of a timelike ruled surface.

  8. Closed timelike curves in asymmetrically warped brane universes

    Science.gov (United States)

    Päs, Heinrich; Pakvasa, Sandip; Dent, James; Weiler, Thomas J.

    2009-08-01

    In asymmetrically-warped spacetimes different warp factors are assigned to space and to time. We discuss causality properties of these warped brane universes and argue that scenarios with two extra dimensions may allow for timelike curves which can be closed via paths in the extra-dimensional bulk. In particular, necessary and sufficient conditions on the metric for the existence of closed timelike curves are presented. We find a six-dimensional warped metric which satisfies the CTC conditions, and where the null, weak and dominant energy conditions are satisfied on the brane (although only the former remains satisfied in the bulk). Such scenarios are interesting, since they open the possibility of experimentally testing the chronology protection conjecture by manipulating on our brane initial conditions of gravitons or hypothetical gauge-singlet fermions (“sterile neutrinos”) which then propagate in the extra dimensions.

  9. Focusing of geodesic congruences in an accelerated expanding Universe

    International Nuclear Information System (INIS)

    Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la

    2012-01-01

    We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds

  10. Focusing of geodesic congruences in an accelerated expanding Universe

    Energy Technology Data Exchange (ETDEWEB)

    Albareti, F.D.; Cembranos, J.A.R. [Departamento de Física Teórica I, Universidad Complutense de Madrid, Ciudad Universitaria, E-28040 Madrid (Spain); Cruz-Dombriz, A. de la, E-mail: fdalbareti@estumail.ucm.es, E-mail: cembra@fis.ucm.es, E-mail: alvaro.delacruz-dombriz@uct.ac.za [Astrophysics, Cosmology and Gravity Centre (ACGC), University of Cape Town, 7701 Rondebosch, Cape Town (South Africa)

    2012-12-01

    We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds.

  11. Geodesic in Godel type universes

    International Nuclear Information System (INIS)

    Galvao, M.O.

    1985-01-01

    We find out the timelike and null geodesics of a certain family of Goedel-like universes, carrying out, at first, a qualitative analysis through the method of the effective potential and, subsequently, proceeding to the exact integration of the equations of motion. (author) [pt

  12. Geodesic flows in a charged black hole spacetime with quintessence

    Energy Technology Data Exchange (ETDEWEB)

    Nandan, Hemwati [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Uniyal, Rashmi [Gurukul Kangri Vishwavidyalaya, Department of Physics, Haridwar, Uttarakhand (India); Government Degree College, Department of Physics, Tehri Garhwal, Uttarakhand (India)

    2017-08-15

    We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordstroem and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly. (orig.)

  13. Geodesic flows in a charged black hole spacetime with quintessence

    International Nuclear Information System (INIS)

    Nandan, Hemwati; Uniyal, Rashmi

    2017-01-01

    We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordstroem and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly. (orig.)

  14. Singularities in geodesic surface congruence

    International Nuclear Information System (INIS)

    Cho, Yong Seung; Hong, Soon-Tae

    2008-01-01

    In the stringy cosmology, we investigate singularities in geodesic surface congruences for the timelike and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the timelike and null string congruences produce the same inequality equation.

  15. The Jacobi metric for timelike geodesics in static spacetimes

    Science.gov (United States)

    Gibbons, G. W.

    2016-01-01

    It is shown that the free motion of massive particles moving in static spacetimes is given by the geodesics of an energy-dependent Riemannian metric on the spatial sections analogous to Jacobi's metric in classical dynamics. In the massless limit Jacobi's metric coincides with the energy independent Fermat or optical metric. For stationary metrics, it is known that the motion of massless particles is given by the geodesics of an energy independent Finslerian metric of Randers type. The motion of massive particles is governed by neither a Riemannian nor a Finslerian metric. The properies of the Jacobi metric for massive particles moving outside the horizon of a Schwarschild black hole are described. By constrast with the massless case, the Gaussian curvature of the equatorial sections is not always negative.

  16. Closed Timelike Curves in Type II Non-Vacuum Spacetime

    International Nuclear Information System (INIS)

    Ahmed, Faizuddin

    2017-01-01

    Here we present a cyclicly symmetric non-vacuum spacetime, admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time-machine spacetime. The spacetime is asymptotically flat, free-from curvature singularities and a four-dimensional extension of the Misner space in curved spacetime. The spacetime is of type II in the Petrov classification scheme and the matter field pure radiation satisfy the energy condition. (paper)

  17. Influence of geometry variations on the gravitational focusing of timelike geodesic congruences

    Science.gov (United States)

    Seriu, Masafumi

    2015-10-01

    We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry variations, characterized by an arbitrary function f (x ), and see that the formulas get simplified to a great extent. We investigate the response of the convergence properties of geodesics in the latest phase of gravitational contractions by restricting the class of conformal geometry variations to the one satisfying the strong energy condition. We then find out that in the final stage, f and D .D f control the overall contraction behavior and that the contraction rate gets larger when f is negative and |f | is so large as to overwhelm |D .D f |. (Here D .D is the Laplacian operator on the spatial hypersurfaces orthogonal to the geodesic congruence in concern.) To get more concrete insights, we also apply the framework to the time-reversed Friedmann-Robertson-Walker model as the simplest case of the singularity formations.

  18. Geodesic congruences in warped spacetimes

    International Nuclear Information System (INIS)

    Ghosh, Suman; Dasgupta, Anirvan; Kar, Sayan

    2011-01-01

    In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum anti-de Sitter geometry without and with branes, we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

  19. Stability of geodesic imcompleteness for Robertson-Walker space-times

    International Nuclear Information System (INIS)

    Beem, J.K.

    1981-01-01

    Let (M,g) be a Lorentzian warped product space-time M = (a, b) X H,g = -dt 2 x fh, where -infinity -infinity and (H,h) is homogeneous, then the past incompleteness of every timelike geodesic of (M,g) is stable under small C 0 perturbations in the space Lor(M) of Lorentzian metrics for M. Also it is shown that if (H,h) is isotropic and (M,g) contains a past-inextendible, past-incomplete null geodesic, then the past incompleteness of all null geodesics is stable under small C 1 perturbations in Lor(M). Given either the isotropy or homogeneity of the Riemannian factor, the background space-time (M,g) is globally hyperbolic. The results of this paper, in particular, answer a question raised by D. Lerner for big bang Robertson-Walker cosmological models affirmatively. (author)

  20. Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes

    International Nuclear Information System (INIS)

    Kubiznak, David; Frolov, Valeri P.; Connell, Patrick; Krtous, Pavel

    2009-01-01

    In [arXiv:0803.3259] the equations describing the parallel transport of orthonormal frames along timelike (spacelike) geodesics in a spacetime admitting a nondegenerate principal conformal Killing-Yano 2-form h were solved. The construction employed is based on studying the Darboux subspaces of the 2-form F obtained as a projection of h along the geodesic trajectory. In this paper we demonstrate that, although slightly modified, a similar construction is possible also in the case of null geodesics. In particular, we explicitly construct the parallel-transported frames along null geodesics in D=4, 5, 6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport along principal null directions in these spacetimes. Such directions coincide with the eigenvectors of the principal conformal Killing-Yano tensor. Finally, we show how to obtain a parallel-transported frame along null geodesics in the background of the 4D Plebanski-Demianski metric which admits only a conformal generalization of the Killing-Yano tensor.

  1. Timelike Killing spinors in seven dimensions

    International Nuclear Information System (INIS)

    Cariglia, Marco; Conamhna, Oisin A.P. Mac

    2004-01-01

    We employ the G-structure formalism to study supersymmetric solutions of minimal and SU(2) gauged supergravities in seven dimensions admitting Killing spinors with an associated timelike Killing vector. The most general such Killing spinor defines a SU(3) structure. We deduce necessary and sufficient conditions for the existence of a timelike Killing spinor on the bosonic fields of the theories, and find that such configurations generically preserve one out of 16 supersymmetries. Using our general supersymmetric ansatz we obtain numerous new solutions, including squashed or deformed anti-de Sitter solutions of the gauged theory, and a large class of Goedel-like solutions with closed timelike curves

  2. DUAL TIMELIKE NORMAL AND DUAL TIMELIKE SPHERICAL CURVES IN DUAL MINKOWSKI SPACE

    OpenAIRE

    ÖNDER, Mehmet

    2009-01-01

    Abstract: In this paper, we give characterizations of dual timelike normal and dual timelike spherical curves in the dual Minkowski 3-space and we show that every dual timelike normal curve is also a dual timelike spherical curve. Keywords: Normal curves, Dual Minkowski 3-Space, Dual Timelike curves. Mathematics Subject Classifications (2000): 53C50, 53C40. DUAL MINKOWSKI UZAYINDA DUAL TIMELIKE NORMAL VE DUAL TIMELIKE KÜRESEL EĞRİLER Özet: Bu çalışmada, dual Minkowski 3-...

  3. Stationary closed strings in five-dimensional flat spacetime

    Science.gov (United States)

    Igata, Takahisa; Ishihara, Hideki; Nishiwaki, Keisuke

    2012-11-01

    We investigate stationary rotating closed Nambu-Goto strings in five-dimensional flat spacetime. The stationary string is defined as a world sheet that is tangent to a timelike Killing vector. The Nambu-Goto equation of motion for the stationary string is reduced to the geodesic equation on the orbit space of the isometry group action generated by the Killing vector. We take a linear combination of a time-translation vector and space-rotation vectors as the Killing vector, and explicitly construct general solutions of stationary rotating closed strings in five-dimensional flat spacetime. We show a variety of their configurations and properties.

  4. Exact string theory model of closed timelike curves and cosmological singularities

    International Nuclear Information System (INIS)

    Johnson, Clifford V.; Svendsen, Harald G.

    2004-01-01

    We study an exact model of string theory propagating in a space-time containing regions with closed timelike curves (CTCs) separated from a finite cosmological region bounded by a big bang and a big crunch. The model is an nontrivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of α ' corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by timelike curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in general relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-big bang cosmological scenarios

  5. On certain geodesic conjugacies of flat cylinders

    Indian Academy of Sciences (India)

    Moreover, these base points must lie on different parallels. By continuity of F ◦α we conclude that the above parallel geodesics fill out a neighborhood of (r0, 0) in S. We conclude that f (r) = 0 for all r close to r0. This proves that R \\ A must be open. D. We call a closed geodesic slant if it is not a parallel geodesic. We have the ...

  6. On Closed Timelike Curves and Warped Brane World Models

    Directory of Open Access Journals (Sweden)

    Slagter Reinoud Jan

    2013-09-01

    Full Text Available At first glance, it seems possible to construct in general relativity theory causality violating solutions. The most striking one is the Gott spacetime. Two cosmic strings, approaching each other with high velocity, could produce closed timelike curves. It was quickly recognized that this solution violates physical boundary conditions. The effective one particle generator becomes hyperbolic, so the center of mass is tachyonic. On a 5-dimensional warped spacetime, it seems possible to get an elliptic generator, so no obstruction is encountered and the velocity of the center of mass of the effective particle has an overlap with the Gott region. So a CTC could, in principle, be constructed. However, from the effective 4D field equations on the brane, which are influenced by the projection of the bulk Weyl tensor on the brane, it follows that no asymptotic conical space time is found, so no angle deficit as in the 4D counterpart model. This could also explain why we do not observe cosmic strings.

  7. Quantum field theory in spaces with closed time-like curves

    International Nuclear Information System (INIS)

    Boulware, D.G.

    1992-01-01

    Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon

  8. Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

    Energy Technology Data Exchange (ETDEWEB)

    Balakrishna, Jayashree [Department of Mathematics and Natural Sciences, College of Arts and Sciences, Harris-Stowe State University, St. Louis, MO (United States); Bondarescu, Ruxandra [Department of Physics, University of Zurich, Zurich (Switzerland); Moran, Christine C., E-mail: corbett@tapir.caltech.edu [TAPIR, Department of Theoretical Astrophysics, California Institute of Technology, Pasadena, CA (United States)

    2016-11-25

    We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

  9. Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

    International Nuclear Information System (INIS)

    Balakrishna, Jayashree; Bondarescu, Ruxandra; Moran, Christine C.

    2016-01-01

    We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

  10. Efficiently computing exact geodesic loops within finite steps.

    Science.gov (United States)

    Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

    2012-06-01

    Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

  11. Kastor-Traschen black holes, null geodesics and conformal circles

    International Nuclear Information System (INIS)

    Casey, Stephen

    2012-01-01

    The Kastor-Traschen metric is a time-dependent solution of the Einstein-Maxwell equations with positive cosmological constant Λ which can be used to describe an arbitrary number of charged dynamical black holes. In this paper, we consider the null geodesic structure of this solution, in particular, focusing on the projection to the space of orbits of the timelike conformal retraction. It is found that these projected light rays arise as integral curves of a system of third-order ordinary differential equations. This system is not uniquely defined, however, and we use the inherent freedom to construct a new system whose integral curves coincide with the projection of distinguished null curves of Kastor-Traschen arising from a magnetic flow. We discuss our results in the one-centre case and demonstrate a link to conformal circles in the limit Λ → 0. We also show how to construct analytic expressions for the projected null geodesics of this metric by exploiting a well-known diffeomorphism between the K-T metric and extremal Reissner-Nordstrom-de Sitter. We make some remarks about the two-centre solution and demonstrate a link with the one-centre case. (paper)

  12. Statistics of geodesics in large quadrangulations

    International Nuclear Information System (INIS)

    Bouttier, J; Guitter, E

    2008-01-01

    We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the case of quadrangulations with a marked geodesic, leading to the notion of 'spine trees', amenable to a direct enumeration. We obtain the generating functions for quadrangulations with a marked geodesic of fixed length, as well as with a set of 'confluent geodesics', i.e. a collection of non-intersecting minimal paths connecting two given points. In the limit of quadrangulations with a large area n, we find in particular an average number 3 x 2 i of geodesics between two fixed points at distance i >> 1 from each other. We show that, for generic endpoints, two confluent geodesics remain close to each other and have an extensive number of contacts. This property fails for a few 'exceptional' endpoints which can be linked by truly distinct geodesics. Results are presented both in the case of finite length i and in the scaling limit i ∼ n 1/4 . In particular, we give the scaling distribution of the exceptional points

  13. Geodesic patterns

    KAUST Repository

    Pottmann, Helmut; Huang, Qixing; Deng, Bailin; Schiftner, Alexander; Kilian, Martin; Guibas, Leonidas J.; Wallner, Johannes

    2010-01-01

    Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.

  14. Geodesic patterns

    KAUST Repository

    Pottmann, Helmut

    2010-07-26

    Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.

  15. Geodesics in Goedel-type space-times

    International Nuclear Information System (INIS)

    Calvao, M.O.; Soares, I.D.; Tiomno, J.

    1988-01-01

    The geodesic curves of the homogeneous Goedel-type space-times, which constitute a two-parameter ({ l and Ω}) class of solutions presented to several theories of gravitation (general relativity, Einstein-Cartan and higher derivative) are investigated. The qualitative properties of those curves by means of the introduction of an effective potential and then accomplish the analytical integration of the equations of motion are examined. It is shown that some of the qualitative features of the free motion in Godel's universe (l 2 =2Ω 2 ) are preserved in all space-times, namely the projections of the geodesics onto the 2-surface (r,ψ) are simple closed curves, and the geodesics for which the ratio of azymuthal angular momentum to total energy, υ is equal to zero always cross the origin r = o. However, two new cases appear: (i) radially unbounded geodesics with υ assuming any (real) value, which may occur only for the causal space-times (l 2 ≥ 4 Ω 2 ), and (ii) geodesics with υ bounded both below and above, which always occur for the circular family (l 2 [pt

  16. Higher-order geodesic deviations applied to the Kerr metric

    CERN Document Server

    Colistete, R J; Kerner, R

    2002-01-01

    Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a general relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this method to the problem of closed orbital motion of test particles in the Kerr metric spacetime. With a simple circular orbit in the equatorial plane taken as the initial geodesic, we obtain finite eccentricity orbits in the form of Taylor series with the eccentricity playing the role of a small parameter. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme gives best results when applied to orbits with low eccentricities, but with arbitrary possible values of (GM/Rc sup 2).

  17. Repulsive and attractive timelike singularities in vacuum cosmologies

    International Nuclear Information System (INIS)

    Miller, B.D.

    1979-01-01

    Spherically symmetric cosmologies whose big bang is partially spacelike and partially timelike are constrained to occur only in the presence of certain types of matter, and in such cosmologies the timelike part of the big bang is a negative-mass singularity. In this paper examples are given of cylindrically symmetric cosmologies whose big bang is partially spacelike and partially timelike. These cosmologies are vacuum. In some of them, the timelike part of the big bang is clearly a (generalized) negative-mass singularity, while in others it is a (generalized) positive-mass singularity

  18. 2T Physics, Weyl Symmetry and the Geodesic Completion of Black Hole Backgrounds

    Science.gov (United States)

    Araya Quezada, Ignacio Jesus

    behavior of fields, interpreted as the first quantized particle wavefunctions in the backgrounds is discussed for the 2D stringy BH case. It is shown that the geodesic completion also carries through at the quantum level, by examining the effective potential of the corresponding Schwarzschild problem. Also, in the case of the 2D stringy BH, it is explicitly shown that the spacetime has a multi-sheeted structure, which resolves possible issues like the presence of closed timelike curves. This multi-sheeted structure is conjectured to exist also for the 4D Schwarzschild BH (and perhaps for all BH backgrounds). The main new results of this thesis are the extended network of dualities, in the form of canonical transformations including time and energy, between the 1T dynamical systems, presented in Chapter 2 and the construction of the geodesically complete 4D Schwarzschild and 2D stringy black hole backgrounds, presented in Chapter 3.

  19. NNLO time-like splitting functions in QCD

    International Nuclear Information System (INIS)

    Moch, S.; Vogt, A.

    2008-07-01

    We review the status of the calculation of the time-like splitting functions for the evolution of fragmentation functions to the next-to-next-to-leading order in perturbative QCD. By employing relations between space-like and time-like deep-inelastic processes, all quark-quark and the gluon-gluon time-like splitting functions have been obtained to three loops. The corresponding quantities for the quark-gluon and gluon-quark splitting at this order are presently still unknown except for their second Mellin moments. (orig.)

  20. The trace formula and the distribution of eigenvalues of Schroedinger operators on manifolds all of whose geodesics are closed

    International Nuclear Information System (INIS)

    Schubert, R.

    1995-05-01

    We investigate the behaviour of the remainder term R(E) in the Weyl formula {nvertical stroke E n ≤E}=Vol(M).E d/2 /[(4π) d/2 Γ(d/2+1)]+R(E) for the eigenvalues E n of a Schroedinger operator on a d-dimensional compact Riemannian manifold all of whose geodesics are closed. We show that R(E) is of the form E (d-1)/2 Θ(√E), where Θ(x) is an almost periodic function of Besicovitch class B 2 which has a limit distribution whose density is a box-shaped function. Furthermore we derive a trace formula and study higher order terms in the asymptotics of the coefficients related to the periodic orbits. The periodicity of the geodesic flow leads to a very simple structure of the trace formula which is the reason why the limit distribution can be computed explicitly. (orig.)

  1. Timelike symmetry of the quantum transition and Einstein-Podolsky-Rosen paradox

    International Nuclear Information System (INIS)

    Costa de Beauregard, Olivier

    1976-01-01

    The non-locality in the paradox is very close to that of Feynman's electron-positron system: the sum of two timelike vectors with 4th components of opposite signs may be spacelike. The intrinsic time symmetry of the quantum transition consists in the presence of both the delayed and the advanced wave inside the ''collapsed'' wave [fr

  2. Spherical null geodesics of rotating Kerr black holes

    International Nuclear Information System (INIS)

    Hod, Shahar

    2013-01-01

    The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r ph (a/M;cosi) of these spherical null geodesics, where a/M is the dimensionless angular momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cosi=±1) are characterized by a monotonic dependence of their radii r ph (a/M;cosi=±1) on the dimensionless spin-parameter a/M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (3√(3)−√(59))/4≲cosi ph (a/M;cosi=const) on the dimensionless rotation-parameter a/M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cosi=√(4/7), above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.

  3. Supergravity on an Atiyah-Hitchin base

    International Nuclear Information System (INIS)

    Stotyn, Sean; Mann, R.B.

    2008-01-01

    We construct solutions to five dimensional minimal supergravity using an Atiyah-Hitchin base space. In examining the structure of solutions we show that they generically contain a singularity either on the Atiyah-Hitchin bolt or at larger radius where there is a singular solitonic boundary. However for most points in parameter space the solution exhibits a velocity of light surface (analogous to what appears in a Goedel space-time) that shields the singularity. For these solutions, all closed time-like curves are causally disconnected from the rest of the space-time in that they exist within the velocity of light surface, which null geodesics are unable to cross. The singularities in these solutions are thus found to be hidden behind the velocity of light surface and so are not naked despite the lack of an event horizon. Outside of this surface the space-time is geodesically complete, asymptotically flat and can be arranged so as not to contain closed time-like curves at infinity. The rest of parameter space simply yields solutions with naked singularities.

  4. Timelike single-logarithm-resummed splitting functions

    Energy Technology Data Exchange (ETDEWEB)

    Albino, S.; Bolzoni, P.; Kniehl, B.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kotikov, A.V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics

    2011-08-15

    We calculate the single logarithmic contributions to the quark singlet and gluon matrix of timelike splitting functions at all orders in the modified minimal-subtraction (MS) scheme. We fix two of the degrees of freedom of this matrix from the analogous results in the massive-gluon regularization scheme by using the relation between that scheme and the MS scheme. We determine this scheme transformation from the double logarithmic contributions to the timelike splitting functions and the coefficient functions of inclusive particle production in e{sup +}e{sup -} annihilation now available in both schemes. The remaining two degrees of freedom are fixed by reasonable physical assumptions. The results agree with the fixed-order results at next-to-next-to-leading order in the literature. (orig.)

  5. On geodesics in low regularity

    Science.gov (United States)

    Sämann, Clemens; Steinbauer, Roland

    2018-02-01

    We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle interrelation with solutions of the geodesic equations. Then we turn to the initial value problem for geodesics for locally Lipschitz continuous metrics and generalize recent results on existence, regularity and uniqueness of solutions in the sense of Filippov.

  6. Fermat principles in general relativity and the existence of light rays on Lorentzian manifolds

    International Nuclear Information System (INIS)

    Fortunato, D.; Masiello, A.

    1995-01-01

    In this paper we review some results on the existence and multiplicity of null geodesics (light rays) joining a point with a timelike curve on a Lorentzian manifold. Moreover a Morse Theory for such geodesics is presented. A variational principle, which is a variant of the classical Fermat principle in optics, allows to characterize the null geodesics joining a point with a timelike curve as the critical points of a functional on an infinite dimensional manifold. Global variational methods are used to get the existence results and Morse Theory. Such results cover a class of Lorentzian manifolds including Schwarzschild, Reissner-Nordstroem and Kerr space-time. (author)

  7. Morse theory on timelike and causal curves

    International Nuclear Information System (INIS)

    Everson, J.; Talbot, C.J.

    1976-01-01

    It is shown that the set of timelike curves in a globally hyperbolic space-time manifold can be given the structure of a Hilbert manifold under a suitable definition of 'timelike.' The causal curves are the topological closure of this manifold. The Lorentzian energy (corresponding to Milnor's energy, except that the Lorentzian inner product is used) is shown to be a Morse function for the space of causal curves. A fixed end point index theorem is obtained in which a lower bound for the index of the Hessian of the Lorentzian energy is given in terms of the sum of the orders of the conjugate points between the end points. (author)

  8. Space- and time-like superselection rules in conformal quantum field theory

    International Nuclear Information System (INIS)

    Schroer, Bert

    2000-11-01

    In conformally invariant quantum field theories one encounters besides the standard DHR superselection theory based on spacelike (Einstein-causal) commutation relations and their Haag duality another timelike (Huygens) based superselection structure. Whereas the DHR theory based on spacelike causality of observables confirmed the Lagrangian internal symmetry picture on the level of the physical principles of local quantum physics, the attempts to understand the timelike based superselection charges associated with the center of the conformal covering group in terms of timelike localized charges lead to a more dynamical role of charges outside the DR theorem and even outside the Coleman-Mandula setting. The ensuing plektonic timelike structure of conformal theories explains the spectrum of the anomalous scale dimensions in terms of admissible braid group representations, similar to the explanation of the possible anomalous spin spectrum expected from the extension of the DHR theory to stringlike d=1+2 plektonic fields. (author)

  9. Geodesics in (Rn, d1

    Directory of Open Access Journals (Sweden)

    Mehmet KILIÇ

    2016-09-01

    Full Text Available The notion of geodesic, which may be regarded as an extension of the line segment in Euclidean geometry to the space we study in, has an important place in many branches of geometry, such as Riemannian geometry, Metric geometry, to name but a few. In this article, the concept of geodesic in a metric space will be introduced, then geodesics in the space (Rn, d1 will be characterized. Furthermore, some examples will be presented to demonstrate the effectiveness of the main result.

  10. Reference results for time-like evolution up to

    Science.gov (United States)

    Bertone, Valerio; Carrazza, Stefano; Nocera, Emanuele R.

    2015-03-01

    We present high-precision numerical results for time-like Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution in the factorisation scheme, for the first time up to next-to-next-to-leading order accuracy in quantum chromodynamics. First, we scrutinise the analytical expressions of the splitting functions available in the literature, in both x and N space, and check their mutual consistency. Second, we implement time-like evolution in two publicly available, entirely independent and conceptually different numerical codes, in x and N space respectively: the already existing APFEL code, which has been updated with time-like evolution, and the new MELA code, which has been specifically developed to perform the study in this work. Third, by means of a model for fragmentation functions, we provide results for the evolution in different factorisation schemes, for different ratios between renormalisation and factorisation scales and at different final scales. Our results are collected in the format of benchmark tables, which could be used as a reference for global determinations of fragmentation functions in the future.

  11. Time travel in Goedel's space

    International Nuclear Information System (INIS)

    Pfarr, J.

    1981-01-01

    An analysis is presented of the motion of test particles in Goedel's universe. Both geodesical and nongeodesical motions are considered; the accelerations for nongeodesical motions are given. Examples for closed timelike world lines are shown and the dynamical conditions for time travel in Goedel's space-time are discussed. It is shown that these conditions alone do not suffice to exclude time travel in Goedel's space-time. (author)

  12. Matrix model and time-like linear dila ton matter

    International Nuclear Information System (INIS)

    Takayanagi, Tadashi

    2004-01-01

    We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)

  13. Diffeomorphometry and geodesic positioning systems for human anatomy.

    Science.gov (United States)

    Miller, Michael I; Younes, Laurent; Trouvé, Alain

    2014-03-01

    The Computational Anatomy project has largely been a study of large deformations within a Riemannian framework as an efficient point of view for generating metrics between anatomical configurations. This approach turns D'Arcy Thompson's comparative morphology of human biological shape and form into a metrizable space. Since the metric is constructed based on the geodesic length of the flows of diffeomorphisms connecting the forms, we call it diffeomorphometry . Just as importantly, since the flows describe algebraic group action on anatomical submanifolds and associated functional measurements, they become the basis for positioning information, which we term geodesic positioning . As well the geodesic connections provide Riemannian coordinates for locating forms in the anatomical orbit, which we call geodesic coordinates . These three components taken together - the metric, geodesic positioning of information, and geodesic coordinates - we term the geodesic positioning system . We illustrate via several examples in human and biological coordinate systems and machine learning of the statistical representation of shape and form.

  14. Geodesics in thermodynamic state spaces of quantum gases

    International Nuclear Information System (INIS)

    Oshima, H.; Obata, T.; Hara, H.

    2002-01-01

    The geodesics for ideal quantum gases are numerically studied. We show that 30 ideal quantum state is connected to an ideal classical state by geodesics and that the bundle of geodesics for Bose gases have a tendency of convergence

  15. Congruences of totally geodesic surfaces

    International Nuclear Information System (INIS)

    Plebanski, J.F.; Rozga, K.

    1989-01-01

    A general theory of congruences of totally geodesic surfaces is presented. In particular their classification, based on the properties of induced affine connections, is provided. In the four-dimensional case canonical forms of the metric tensor admitting congruences of two-dimensional totally geodesic surfaces of rank one are given. Finally, congruences of two-dimensional extremal surfaces are studied. (author)

  16. Geodesic exponential kernels: When Curvature and Linearity Conflict

    DEFF Research Database (Denmark)

    Feragen, Aase; Lauze, François; Hauberg, Søren

    2015-01-01

    manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic...

  17. Geodesic distance in planar graphs

    International Nuclear Information System (INIS)

    Bouttier, J.; Di Francesco, P.; Guitter, E.

    2003-01-01

    We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy

  18. Craniofacial Reconstruction Evaluation by Geodesic Network

    Directory of Open Access Journals (Sweden)

    Junli Zhao

    2014-01-01

    Full Text Available Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the original face are built, respectively, by geodesics and isogeodesics, whose intersections are network vertices. Then, the absolute value of the correlation coefficient of the features of all corresponding geodesic network vertices between two models is taken as the holistic similarity, where the weighted average of the shape index values in a neighborhood is defined as the feature of each network vertex. Moreover, the geodesic network vertices of each model are divided into six subareas, that is, forehead, eyes, nose, mouth, cheeks, and chin, and the local similarity is measured for each subarea. Experiments using 100 pairs of reconstructed craniofacial faces and their corresponding original faces show that the evaluation by our method is roughly consistent with the subjective evaluation derived from thirty-five persons in five groups.

  19. A regularized approach for geodesic-based semisupervised multimanifold learning.

    Science.gov (United States)

    Fan, Mingyu; Zhang, Xiaoqin; Lin, Zhouchen; Zhang, Zhongfei; Bao, Hujun

    2014-05-01

    Geodesic distance, as an essential measurement for data dissimilarity, has been successfully used in manifold learning. However, most geodesic distance-based manifold learning algorithms have two limitations when applied to classification: 1) class information is rarely used in computing the geodesic distances between data points on manifolds and 2) little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances. In this paper, we regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed. The method consists of three techniques: a semisupervised graph construction method, replacement of original data points with feature vectors which are built by geodesic distances, and a new semisupervised dimension reduction method for feature vectors. Experiments on the MNIST, USPS handwritten digit data sets, MIT CBCL face versus nonface data set, and an intelligent traffic data set show the effectiveness of the proposed algorithm.

  20. Vacuum non-expanding horizons and shear-free null geodesic congruences

    International Nuclear Information System (INIS)

    Adamo, T M; Newman, E T

    2009-01-01

    We investigate the geometry of a particular class of null surfaces in spacetime called vacuum non-expanding horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex worldline in a complex four-dimensional space, each such choice induces a CR structure on the horizon, and a particular worldline (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.

  1. Covariant description of kinetic freeze-out through a finite time-like layer

    International Nuclear Information System (INIS)

    Molnar, E; Csernai, L P; Magas, V K; Lazar, Zs I; NyIri, A; Tamosiunas, K

    2007-01-01

    The freeze-out (FO) problem is addressed for a covariant FO probability and a finite FO layer with a time-like normal vector continuing the line of studies introduced in Molnar et al (2006 Phys. Rev. C 74 024907). The resulting post-FO momentum distribution functions are presented and discussed. We show that in general the post-FO distributions are non-thermal and asymmetric distributions even for time-like FO situations

  2. Timelike naked singularity

    International Nuclear Information System (INIS)

    Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis

    2004-01-01

    We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture

  3. Symmetries and conserved quantities in geodesic motion

    International Nuclear Information System (INIS)

    Hojman, S.; Nunez, L.; Patino, A.; Rago, H.

    1986-01-01

    Recently obtained results linking several constants of motion to one (non-Noetherian) symmetry to the problem of geodesic motion in Riemannian space-times are applied. The construction of conserved quantities in geodesic motion as well as the deduction of geometrical statements about Riemannian space-times are achieved

  4. Global energy-momentum conservation in general relativity

    International Nuclear Information System (INIS)

    Nissani, N.; Leibowitz, E.

    1989-01-01

    It is shown that there exists a family of coordinate systems in which the energy-momentum tensor is globally conserved. Furthermore, this preferred class of frames includes geodesic systems with respect to any arbitrary point or timelike geodesic line. This implies a physically satisfactory conservation law with no need to introduce an extraneous pseudotensor

  5. On the geodesic incompleteness of spacetimes containing marginally (outer) trapped surfaces

    International Nuclear Information System (INIS)

    Costa e Silva, I P

    2012-01-01

    In a recent paper, Eichmair et al (2012 arXiv:1204.0278v1) have proved a Gannon–Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. A natural question is whether the corresponding incomplete geodesics could still be complete in a possible non-globally hyperbolic extension of spacetime. In this paper, some variants of their result are given with weaker causality assumptions, thus suggesting that the answer is generically negative, at least if the putative extension has no closed timelike curves. We consider first marginally trapped surfaces (MTS) in chronological spacetimes, introducing the natural notion of a generic MTS, a notion also applicable to MOTS. In particular, a Hawking–Penrose-type singularity theorem is proven in chronological spacetimes with dimension n ⩾ 3 containing a generic MTS. Such surfaces naturally arise as cross-sections of quasi-local generalizations of black hole horizons, such as dynamical and trapping horizons, and we discuss some natural conditions which ensure the existence of MTS in initial data sets. Nevertheless, much of the more recent literature has focused on MOTS rather than MTS as quasi-local substitutes for the description of black holes, as they are arguably more natural and easier to handle in a number of situations. It is therefore pertinent to ask to what extent one can deduce the existence of singularities in the presence of MOTS alone. We address this issue and show that singularities indeed arise in the presence of generic MOTS, but under slightly stronger causal conditions than those in the case of MTS (specifically, for causally simple spacetimes). On the other hand, we show that with additional conditions on the MOTS itself, namely that it is either the boundary of a compact spatial region, or strictly stable in a suitable sense, a Penrose–Hawking-type singularity theorem can still be established for

  6. Principal normal indicatrices of closed space curves

    DEFF Research Database (Denmark)

    Røgen, Peter

    1999-01-01

    A theorem due to J. Weiner, which is also proven by B. Solomon, implies that a principal normal indicatrix of a closed space curve with nonvanishing curvature has integrated geodesic curvature zero and contains no subarc with integrated geodesic curvature pi. We prove that the inverse problem alw...

  7. Craniofacial Reconstruction Evaluation by Geodesic Network

    OpenAIRE

    Zhao, Junli; Liu, Cuiting; Wu, Zhongke; Duan, Fuqing; Wang, Kang; Jia, Taorui; Liu, Quansheng

    2014-01-01

    Craniofacial reconstruction is to estimate an individual’s face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the or...

  8. Single-Spin Polarization Effects and the Determination of Timelike Proton Form Factors

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, S

    2003-10-24

    We show that measurements of the proton's polarization in e{sup +}e{sup -} {yields} p{bar p} strongly discriminate between analytic forms of models which fit the proton form factors in the spacelike region. In particular, the single-spin asymmetry normal to the scattering plane measures the relative phase difference between the timelike G{sub E} and G{sub M} form factors. The expected proton polarization in the timelike region is large, of order of several tens of percent.

  9. Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

    Directory of Open Access Journals (Sweden)

    Sheng-lan Chen

    2014-01-01

    Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.

  10. Geodesic motion and confinement in Goedel's universe

    International Nuclear Information System (INIS)

    Novello, M.; Soares, I.D.; Tiomno, J.

    1982-01-01

    A complete study of geodesic motion in Goedel's universe, using the method of the Effective Potential is presented. It then emerges a clear physical picture of free motion and its stability in this universe. Geodesics of a large class have finite intervals in which the particle moves back in time (dt/ds [pt

  11. Feasibility studies of time-like proton electromagnetic form factors at PANDA-FAIR

    Energy Technology Data Exchange (ETDEWEB)

    Dbeyssi, Alaa; Capozza, Luigi; Deiseroth, Malte; Froehlich, Bertold; Khaneft, Dmitry; Mora Espi, Maria Carmen; Noll, Oliver; Rodriguez Pineiro, David; Valente, Roserio; Zambrana, Manuel; Zimmermann, Iris [Helmholtz-Institut Mainz, Mainz (Germany); Maas, Frank [Helmholtz-Institut Mainz, Mainz (Germany); Institute of Nuclear Physics, Mainz (Germany); PRISMA Cluster of Excellence, Mainz (Germany); Marchand, Dominique; Tomasi-Gustafsson, Egle; Wang, Ying [Institut de Physique Nucleaire, Orsay (France); Collaboration: PANDA-Collaboration

    2015-07-01

    Electromagnetic form factors are fundamental quantities which describe the intrinsic electric and magnetic distributions of hadrons. Time-like proton form factors are experimentally accessible through the annihilation processes anti p+p <-> e{sup +}+e{sup -}. Their measurement in the time-like region had been limited by the low statistics achieved by the experiments. This contribution reports on the results of Monte Carlo simulations for future measurements of electromagnetic proton form factors at PANDA (antiProton ANnihilation at DArmstadt). In frame of the PANDARoot software, the statistical precision at which the proton form factors will be determined is estimated. The signal (anti p+p → e{sup +}+e{sup -}) identification and the suppression of the main background process (anti p+p → π{sup +}+π{sup -}) are studied. Different methods have been used and/or developed to generate and analyse the processes of interest. The results show that time-like proton form factors will be measured at PANDA with unprecedented statistical accuracy.

  12. Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics

    Directory of Open Access Journals (Sweden)

    Liandong Zhang

    2012-01-01

    Full Text Available A novel gait planning method using geodesics for humanoid robot is given in this paper. Both the linear inverted pendulum model and the exact Single Support Phase (SSP are studied in our energy optimal gait planning based on geodesics. The kinetic energy of a 2-dimension linear inverted pendulum is obtained at first. We regard the kinetic energy as the Riemannian metric and the geodesic on this metric is studied and this is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the COG because the kinetic energy along geodesic is invariant according to the geometric property of geodesics and the walking is smooth and energy saving. Then the walking in Single Support Phase is studied and the energy optimal gait for the swing leg is obtained using our geodesics method. Finally, experiments using state-of-the-art method and using our geodesics optimization method are carried out respectively and the corresponding currents of the joint motors are recorded. With the currents comparing results, the feasibility of this new gait planning method is verified.

  13. Towards three-loop QCD corrections to the time-like splitting functions

    International Nuclear Information System (INIS)

    Gituliar, O.; Moch, S.

    2015-05-01

    We report on the status of a direct computation of the time-like splitting functions at next-to-next-to-leading order in QCD. Time-like splitting functions govern the collinear kinematics of inclusive hadron production and the evolution of the parton fragmentation distributions. Current knowledge about them at three loops has been inferred by means of crossing symmetry from their related space-like counterparts, which has left certain parts of the off-diagonal quark-gluon splitting function undetermined. This motivates an independent calculation from first principles. We review the tools and methods which are applied to attack the problem.

  14. Instantons from geodesics in AdS moduli spaces

    Science.gov (United States)

    Ruggeri, Daniele; Trigiante, Mario; Van Riet, Thomas

    2018-03-01

    We investigate supergravity instantons in Euclidean AdS5 × S5/ℤk. These solutions are expected to be dual to instantons of N = 2 quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: for degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts.

  15. Null geodesic deviation II. Conformally flat space--times

    International Nuclear Information System (INIS)

    Peters, P.C.

    1975-01-01

    The equation of geodesic deviation is solved in conformally flat space--time in a covariant manner. The solution is given as an integral equation for general geodesics. The solution is then used to evaluate second derivatives of the world function and derivatives of the parallel propagator, which need to be known in order to find the Green's function for wave equations in curved space--time. A method of null geodesic limits of two-point functions is discussed, and used to find the scalar Green's function as an iterative series

  16. On the structure of space-time caustics

    International Nuclear Information System (INIS)

    Rosquist, K.

    1983-01-01

    Caustics formed by timelike and null geodesics in a space-time M are investigated. Care is taken to distinguish the conjugate points in the tangent space (T-conjugate points) from conjugate points in the manifold (M-conjugate points). It is shown that most nonspacelike conjugate points are regular, i.e. with all neighbouring conjugate points having the same degree of degeneracy. The regular timelike T-conjugate locus is shown to be a smooth 3-dimensional submanifold of the tangent space. Analogously, the regular null T-conjugate locus is shown to be a smooth 2-dimensional submanifold of the light cone in the tangent space. The smoothness properties of the null caustic are used to show that if an observer sees focusing in all directions, then there will necessarily be a cusp in the caustic. If, in addition, all the null conjugate points have maximal degree of degeneracy (as in the closed Friedmann-Robertson-Walker universes), then the space-time is closed. (orig.)

  17. Can an observer really catch up with light?

    International Nuclear Information System (INIS)

    Tian, Guihua; Zheng, Zhao

    2003-01-01

    Given a null geodesic γ 0 (λ) with a point r in (p, q) conjugate to p along γ 0 (λ), up to the second variation, there will be a variation of γ 0 (λ) which will give a timelike curve from p to q. This is the well-known theory proved in the famous book (Hawking S W and Ellis G F R 1973 The Large Scale Structure of Space-Time (Cambridge: Cambridge University Press)). In this paper, we prove that the timelike curves coming from the above-mentioned second variation have a proper acceleration approaching infinity as the timelike curves approach the null geodesic. This means no observer infinitesimally near the light can begin at the same point with it and finally catch up with it. Only when separated from the light path finitely, can the observer begin at the same point with it and really catch up with it

  18. Geodesic detection of Agulhas rings

    Science.gov (United States)

    Beron-Vera, F. J.; Wang, Y.; Olascoaga, M. J.; Goni, G. J.; Haller, G.

    2012-12-01

    Mesoscale oceanic eddies are routinely detected from instantaneous velocities. While simple to implement, this Eulerian approach gives frame-dependent results and often hides true material transport by eddies. Building on the recent geodesic theory of transport barriers, we develop an objective (i.e., frame-independent) method for accurately locating coherent Lagrangian eddies. These eddies act as compact water bodies, with boundaries showing no leakage or filamentation over long periods of time. Applying the algorithm to altimetry-derived velocities in the South Atlantic, we detect, for the first time, Agulhas rings that preserve their material coherence for several months, while eddy candidates yielded by other approaches tend to disperse or leak within weeks. These findings suggest that current Eulerian estimates of the Agulhas leakage need significant revision.Temporal evolution of fluid patches identified as eddies by different methods. First column: eddies extracted using geodesic eddy identification [1,2]. Second column: eddies identified from sea surface height (SSH) using the methodology of Chelton et al. [2] with U/c > 1. Third column: eddies identified as elliptic regions by the Okubo-Weiss (OW) criterion [e.g., 3]. Fourth column: eddies identified as mesoelliptic (ME) regions by Mezic et al.'s [4] criterion. References: [1] Beron-Vera et al. (2012). Geodesic eddy detection suggests reassessment of Agulhas leakage. Proc. Nat. Acad. Sci. USA, submitted. [2] Haller & Beron-Vera (2012). Geodesic theory of transport barriers in two-dimensional flows. Physica D, in press. [2] Chelton et al. (2011). Prog. Oceanog. 91, 167. [3] Chelton et al. (2007). Geophys. Res. Lett. 34, L5606. [4] Mezic et al. (2010). Science 330, 486.

  19. The pion-nucleon form factor in space- and time-like regions

    International Nuclear Information System (INIS)

    Speth, J.; Tegen, R.

    1990-01-01

    We investigate the pion-nucleon vertex function in space- and time-like regions; these vertex functions appear as internal vertices in nucleon-antinucleon annihilations into n pions (n=2, 3, ..., 6). It is emphasised that only relativistic quark models can account for these vertices where one of the baryons/antibaryons is far off-shell with total energy close to zero. Using a novel 4-momentum projection technique we obtain results which generalize the usual (Breit frame) calculation of G πNN (k 2 ) (space-like) thereby removing completely the discrepancy in the Goldberger-Treiman relation. Our relativistic quark model calculation also explains the empirical suppression of antibaryonic contributions to the vertex functions Gsub(πNanti B) and Gsub(πBanti N) which enter in processes like Nanti N→ππ. (orig.)

  20. Reference results for time-like evolution up to O(α_s"3)

    International Nuclear Information System (INIS)

    Bertone, Valerio; Carrazza, Stefano; Nocera, Emanuele R.

    2015-01-01

    We present high-precision numerical results for time-like Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution in the (MS)-bar factorisation scheme, for the first time up to next-to-next-to-leading order accuracy in quantum chromodynamics. First, we scrutinise the analytical expressions of the splitting functions available in the literature, in both x and N space, and check their mutual consistency. Second, we implement time-like evolution in two publicly available, entirely independent and conceptually different numerical codes, in x and N space respectively: the already existing APFEL code, which has been updated with time-like evolution, and the new MELA code, which has been specifically developed to perform the study in this work. Third, by means of a model for fragmentation functions, we provide results for the evolution in different factorisation schemes, for different ratios between renormalisation and factorisation scales and at different final scales. Our results are collected in the format of benchmark tables, which could be used as a reference for global determinations of fragmentation functions in the future.

  1. Form factors and QCD in spacelike and timelike region

    International Nuclear Information System (INIS)

    A.P. Bakulev; A.V. Radyushkin; N.G. Stefanis

    2000-01-01

    The authors analyze the basic hard exclusive processes: πγ * γ-transition, pion and nucleon electromagnetic form factors, and discuss the analytic continuation of QCD formulas from the spacelike q 2 2 > 0 of the relevant momentum transfers. They describe the construction of the timelike version of the coupling constant α s . They show that due to the analytic continuation of the collinear logarithms each eigenfunction of the evolution equation acquires a phase factor and investigate the resulting interference effects which are shown to be very small. They found no sources for the K-factor-type enhancements in the perturbative QCD contribution to the hadronic form factors. To study the soft part of the pion electromagnetic form factor, they use a QCD sum rule inspired model and show that there are non-canceling Sudakov double logarithms which result in a K-factor-type enhancement in the timelike region

  2. Form factors and QCD in spacelike and timelike regions

    International Nuclear Information System (INIS)

    Bakulev, A. P.; Radyushkin, A. V.; Stefanis, N. G.

    2000-01-01

    We analyze the basic hard exclusive processes, the πγ * γ-transition and the pion and nucleon electromagnetic form factors, and discuss the analytic continuation of QCD formulas from the spacelike q 2 2 >0 of the relevant momentum transfers. We describe the construction of the timelike version of the coupling constant α s . We show that due to the analytic continuation of the collinear logarithms, each eigenfunction of the evolution equation acquires a phase factor and investigate the resulting interference effects which are shown to be very small. We find no sources for the K-factor-type enhancements in the perturbative QCD contribution to the hadronic form factors. To study the soft part of the pion electromagnetic form factor, we use a QCD sum rule inspired model and show that there are noncanceling Sudakov double logarithms which result in a K-factor-type enhancement in the timelike region

  3. The geometry of geodesics

    CERN Document Server

    Busemann, Herbert

    2005-01-01

    A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

  4. Kaon transverse charge density from space- and timelike data

    Science.gov (United States)

    Mecholsky, N. A.; Meija-Ott, J.; Carmignotto, M.; Horn, T.; Miller, G. A.; Pegg, I. L.

    2017-12-01

    We used the world data on the kaon form factor to extract the transverse kaon charge density using a dispersion integral of the imaginary part of the kaon form factor in the timelike region. Our analysis includes recent data from e+e- annihiliation measurements extending the kinematic reach of the data into the region of high momentum transfers conjugate to the region of short transverse distances. To calculate the transverse density we created a superset of both timelike and spacelike data and developed an empirical parameterization of the kaon form factor. The spacelike set includes two new data points we extracted from existing cross section data. We estimate the uncertainty on the resulting transverse density to be 5% at b =0.025 fm and significantly better at large distances. New kaon data planned with the 12 GeV Jefferson Lab may have a significant impact on the charge density at distances of b <0.1 fm.

  5. Geodesic congruences in the Palatini f(R) theory

    International Nuclear Information System (INIS)

    Shojai, Fatimah; Shojai, Ali

    2008-01-01

    We shall investigate the properties of a congruence of geodesics in the framework of Palatini f(R) theories. We shall evaluate the modified geodesic deviation equation and the Raychaudhuri's equation and show that f(R) Palatini theories do not necessarily lead to attractive forces. Also, we shall study energy condition for f(R) Palatini gravity via a perturbative analysis of the Raychaudhuri's equation.

  6. Non-integrability of geodesic flow on certain algebraic surfaces

    International Nuclear Information System (INIS)

    Waters, T.J.

    2012-01-01

    This Letter addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface xyz=1. We prove this is the case using the Morales–Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result. -- Highlights: ► The behaviour of geodesics on surfaces defined by algebraic expressions is studied. ► The non-integrability of the geodesic equations is rigorously proved using differential Galois theory. ► Morales–Ramis theory and Kovacic's algorithm is used and the normal variational equation is of Fuchsian type. ► Some extensions and limitations are discussed.

  7. Time travel in the homogeneous Som-Raychaudhuri Universe

    International Nuclear Information System (INIS)

    Paiva, F.M.; Reboucas, M.J.; Teixeira, A.F.F.

    1987-01-01

    Properties of the rotating Som-Raychaudhuri homogeneous space-time are investigated: time-like and null geodesics, causality features, horizons and invariant characterization. An integral representation of its five isometries is also discussed. (author) [pt

  8. Anatomy of geodesic Witten diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Heng-Yu; Kuo, En-Jui [Department of Physics and Center for Theoretical Sciences, National Taiwan University,Taipei 10617, Taiwan (China); Kyono, Hideki [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)

    2017-05-12

    We revisit the so-called “Geodesic Witten Diagrams” (GWDs) https://www.doi.org/10.1007/JHEP01(2016)146, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related “split representation” for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.

  9. First integrals of geodesics in the Einstein-Schwarzschild space

    International Nuclear Information System (INIS)

    Meshkov, A.G.; Dordzhiev, P.B.

    1984-01-01

    Linear and quadratic velocity integrals of geodesics in the Einstein-Schwarzschild space are calculated. The Schwarzschild geodesics equations have only four independent linear integrals. Quadratic integrals are polynomials from linear ones with constant coefficients. Total separation of variables in the Hamilton-Jacobi equation with Schwarzschild metric is possible only in two coordinate systems: ''spherical'' and ''conic'' systems

  10. A visualization of null geodesics for the bonnor massive dipole

    Directory of Open Access Journals (Sweden)

    G. Andree Oliva Mercado

    2015-08-01

    Full Text Available In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.

  11. Semi-local inversion of the geodesic ray transform in the hyperbolic plane

    International Nuclear Information System (INIS)

    Courdurier, Matias; Saez, Mariel

    2013-01-01

    The inversion of the ray transform on the hyperbolic plane has applications in geophysical exploration and in medical imaging techniques (such as electrical impedance tomography). The geodesic ray transform has been studied in more general geometries and including attenuation, but all of the available inversion formulas require knowledge of the ray transform for all the geodesics. In this paper we present a different inversion formula for the ray transform on the hyperbolic plane, which has the advantage of only requiring knowledge of the ray transform in a reduced family of geodesics. The required family of geodesics is directly related to the set where the original function is to be recovered. (paper)

  12. Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures

    Directory of Open Access Journals (Sweden)

    Ishikawa Goo

    2015-06-01

    Full Text Available Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown in (15, that, if the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.

  13. Are eikonal quasinormal modes linked to the unstable circular null geodesics?

    Directory of Open Access Journals (Sweden)

    R.A. Konoplya

    2017-08-01

    Full Text Available In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein–Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein–Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

  14. Are eikonal quasinormal modes linked to the unstable circular null geodesics?

    Science.gov (United States)

    Konoplya, R. A.; Stuchlík, Z.

    2017-08-01

    In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

  15. Superintegrability of geodesic motion on the sausage model

    Science.gov (United States)

    Arutyunov, Gleb; Heinze, Martin; Medina-Rincon, Daniel

    2017-06-01

    Reduction of the η-deformed sigma model on AdS_5× S5 to the two-dimensional squashed sphere (S^2)η can be viewed as a special case of the Fateev sausage model where the coupling constant ν is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the sl(2) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model. This paper is a tribute to the memory of Prof Petr Kulish.

  16. Nucleon electromagnetic structure studies in the spacelike and timelike regions

    International Nuclear Information System (INIS)

    Guttmann, Julia

    2013-01-01

    The thesis investigates the nucleon structure probed by the electromagnetic interaction. One of the most basic observables, reflecting the electromagnetic structure of the nucleon, are the form factors, which have been studied by means of elastic electron-proton scattering with ever increasing precision for several decades. In the timelike region, corresponding with the proton-antiproton annihilation into a electron-positron pair, the present experimental information is much less accurate. However, in the near future high-precision form factor measurements are planned. About 50 years after the first pioneering measurements of the electromagnetic form factors, polarization experiments stirred up the field since the results were found to be in striking contradiction to the findings of previous form factor investigations from unpolarized measurements. Triggered by the conflicting results, a whole new field studying the influence of two-photon exchange corrections to elastic electron-proton scattering emerged, which appeared as the most likely explanation of the discrepancy. The main part of this thesis deals with theoretical studies of two-photon exchange, which is investigated particularly with regard to form factor measurements in the spacelike as well as in the timelike region. An extraction of the two-photon amplitudes in the spacelike region through a combined analysis using the results of unpolarized cross section measurements and polarization experiments is presented. Furthermore, predictions of the two-photon exchange effects on the e + p/e - p cross section ratio are given for several new experiments, which are currently ongoing. The two-photon exchange corrections are also investigated in the timelike region in the process p anti p → e + e - by means of two factorization approaches. These corrections are found to be smaller than those obtained for the spacelike scattering process. The influence of the two-photon exchange corrections on cross section

  17. Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

    Directory of Open Access Journals (Sweden)

    Timothy M. Adamo

    2009-09-01

    Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi’s integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

  18. Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

    Directory of Open Access Journals (Sweden)

    Timothy M. Adamo

    2012-01-01

    Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, H-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi's integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum--conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

  19. Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation.

    Science.gov (United States)

    Adamo, Timothy M; Newman, Ezra T; Kozameh, Carlos

    2012-01-01

    A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, [Formula: see text]-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum-conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

  20. Space–time and spatial geodesic orbits in Schwarzschild geometry

    Science.gov (United States)

    Resca, Lorenzo

    2018-05-01

    Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

  1. Geodesic deviation and Minikowski space

    International Nuclear Information System (INIS)

    Barraco, D.; Kozameh, C.; Newman, E.T.; Tod, P.

    1990-01-01

    The authors study the properties of the solution space of local surface-forming null sub-congruences in the neighborhood of a given null geodesic in a pseudo-Riemannian space-time. This solution space is a three-dimensional manifold, naturally endowed with a conformal Minkowski metric

  2. Geodesics without differential equations: general relativistic calculations for introductory modern physics classes

    International Nuclear Information System (INIS)

    Rowland, D R

    2006-01-01

    Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics

  3. On the role of the magnetic tension during the gravitational collapse of a magnetised fluid

    International Nuclear Information System (INIS)

    Tsagas, Christos G

    2005-01-01

    We investigate the physics of magnetised gravitational collapse by studying the behaviour of a timelike congruence of non-geodesic worldlines in the presence of a magnetic field. We show that the general relativistic coupling between magnetism and geometry, and the tension properties of the field, lead to magneto-curvature stresses that resist the collapse. When these tension stresses dominate, they can prevent an initially converging family of non-geodesic worldlines from focusing without violating the standard energy conditions

  4. On exclusive reactions in the time-like region

    CERN Document Server

    Kroll, P; Schürmann, M; Schweiger, W; Pilsner, Th.

    1993-01-01

    The electromagnetic form factors of the proton in the time-like region and two-photon annihilations into proton-antiproton are investigated. To calculate these processes at moderately large $s$ we use a variant of the Brodsky-Lepage hard-scattering formalism where diquarks are considered as quasi-elementary constituents of baryons. The proton wave function and the parameters controlling the diquark contributions are determined from fits to space-like data. We also comment on the decay $\\eta_c \\to p\\bar{p}$.

  5. Optimized curve design for image analysis using localized geodesic distance transformations

    Science.gov (United States)

    Braithwaite, Billy; Niska, Harri; Pöllänen, Irene; Ikonen, Tiia; Haataja, Keijo; Toivanen, Pekka; Tolonen, Teemu

    2015-03-01

    We consider geodesic distance transformations for digital images. Given a M × N digital image, a distance image is produced by evaluating local pixel distances. Distance Transformation on Curved Space (DTOCS) evaluates shortest geodesics of a given pixel neighborhood by evaluating the height displacements between pixels. In this paper, we propose an optimization framework for geodesic distance transformations in a pattern recognition scheme, yielding more accurate machine learning based image analysis, exemplifying initial experiments using complex breast cancer images. Furthermore, we will outline future research work, which will complete the research work done for this paper.

  6. 3D Facial Similarity Measure Based on Geodesic Network and Curvatures

    Directory of Open Access Journals (Sweden)

    Junli Zhao

    2014-01-01

    Full Text Available Automated 3D facial similarity measure is a challenging and valuable research topic in anthropology and computer graphics. It is widely used in various fields, such as criminal investigation, kinship confirmation, and face recognition. This paper proposes a 3D facial similarity measure method based on a combination of geodesic and curvature features. Firstly, a geodesic network is generated for each face with geodesics and iso-geodesics determined and these network points are adopted as the correspondence across face models. Then, four metrics associated with curvatures, that is, the mean curvature, Gaussian curvature, shape index, and curvedness, are computed for each network point by using a weighted average of its neighborhood points. Finally, correlation coefficients according to these metrics are computed, respectively, as the similarity measures between two 3D face models. Experiments of different persons’ 3D facial models and different 3D facial models of the same person are implemented and compared with a subjective face similarity study. The results show that the geodesic network plays an important role in 3D facial similarity measure. The similarity measure defined by shape index is consistent with human’s subjective evaluation basically, and it can measure the 3D face similarity more objectively than the other indices.

  7. Nucleon electromagnetic structure studies in the spacelike and timelike regions

    Energy Technology Data Exchange (ETDEWEB)

    Guttmann, Julia

    2013-07-23

    The thesis investigates the nucleon structure probed by the electromagnetic interaction. One of the most basic observables, reflecting the electromagnetic structure of the nucleon, are the form factors, which have been studied by means of elastic electron-proton scattering with ever increasing precision for several decades. In the timelike region, corresponding with the proton-antiproton annihilation into a electron-positron pair, the present experimental information is much less accurate. However, in the near future high-precision form factor measurements are planned. About 50 years after the first pioneering measurements of the electromagnetic form factors, polarization experiments stirred up the field since the results were found to be in striking contradiction to the findings of previous form factor investigations from unpolarized measurements. Triggered by the conflicting results, a whole new field studying the influence of two-photon exchange corrections to elastic electron-proton scattering emerged, which appeared as the most likely explanation of the discrepancy. The main part of this thesis deals with theoretical studies of two-photon exchange, which is investigated particularly with regard to form factor measurements in the spacelike as well as in the timelike region. An extraction of the two-photon amplitudes in the spacelike region through a combined analysis using the results of unpolarized cross section measurements and polarization experiments is presented. Furthermore, predictions of the two-photon exchange effects on the e{sup +}p/e{sup -}p cross section ratio are given for several new experiments, which are currently ongoing. The two-photon exchange corrections are also investigated in the timelike region in the process p anti p → e{sup +}e{sup -} by means of two factorization approaches. These corrections are found to be smaller than those obtained for the spacelike scattering process. The influence of the two-photon exchange corrections on

  8. Spacelike and timelike form factors for ω→πγ* and K*→Kγ* in the light-front quark model

    International Nuclear Information System (INIS)

    Choi, Ho-Meoyng

    2008-01-01

    We investigate space- and timelike form factors for ω→πγ* and K*→Kγ* decays using the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The momentum dependent spacelike form factors are obtained in the q + =0 frame and then analytically continued to the timelike region. Our prediction for the timelike form factor F ωπ (q 2 ) is in good agreement with the experimental data. We also find that the spacelike form factor F K* ± K ± (Q 2 ) for charged kaons encounters a zero because of the negative interference between the two currents to the quark and the antiquark.

  9. Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

    Science.gov (United States)

    Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

    2018-06-01

    We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

  10. Some remarks on geodesics in gauge groups and harmonic maps

    International Nuclear Information System (INIS)

    Valli, G.

    1987-08-01

    The following topics are discussed: Euler's equations for geodesics in the gauge groups and in gauge orbits of connections, conserved quantities and moment map, existence and uniqueness of solutions for the Cauchy problem, stationary solutions and harmonic bundles, harmonic gauges on Riemann surfaces and Lax pairs, low geodesics in gauge groups over Riemann surfaces produce, by Hodge decomposition, paths of holomorphic differentials. 19 refs

  11. Geodesics and symmetries of doubly spinning black rings

    International Nuclear Information System (INIS)

    Durkee, Mark

    2009-01-01

    This paper studies various properties of the Pomeransky-Sen'kov doubly spinning black ring spacetime. I discuss the structure of the ergoregion, and then go on to demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics, which exist in the ergoregion. These geodesics are used to construct geometrically motivated coordinates that cover the black hole horizon. Finally, I relate this weak form of separability to the existence of a conformal Killing tensor in a particular four-dimensional spacetime obtained by Kaluza-Klein reduction, and show that a related conformal Killing-Yano tensor only exists in the singly spinning case.

  12. Gauss-Bonnet's Formula and Closed Frenet Frames

    DEFF Research Database (Denmark)

    Røgen, Peter

    1998-01-01

    Our main result is that integrated geodesic curvature of a (non-simple) closed curve on the unit 2-sphere equals a half integer weighted sum of the areas of the connected components of the complement of the curve. These weights that gives a spherical analogy to the winding number of closed plane ...

  13. Geodesics in hypercomplex number systems. Application to commutative quaternions

    International Nuclear Information System (INIS)

    Catoni, Francesco; Zampetti, Paolo; Cannata, Roberto; Bordoni, Luciana

    1997-10-01

    The functions of hypercomplex variable can be related to the physical fields. Following the Einstein's ideas, by which the Theory of General Relativity was developed, they want to verify if a generalisation is possible, in order to described the motion of a body in a gravitational field, by the geodesics in spaces ''deformed'' by functional transformations of hypercomplex variables. These number systems introduce new space symmetries. This paper is just a first step in the more extended study. As a first application they consider the ''commutative quaternions'' system that may be considered as a composition of complex and hyperbolic numbers. By using in this system the same functional transformations valid for the two dimensional case, elliptical geodesics are obtained, with the eccentricity related to the angle between the orbit plane and a reference plane. These geodesics do not describe the Kepler orbits, but they show a space anisotropy that might be related to planet orbits of the solar system

  14. Surfaces foliated by planar geodesics: a model forcurved wood design

    DEFF Research Database (Denmark)

    Brander, David; Gravesen, Jens

    2017-01-01

    Surfaces foliated by planar geodesics are a natural model for surfaces made from wood strips. We outline how to construct all solutions, and produce non-trivial examples, such as a wood-strip Klein bottle......Surfaces foliated by planar geodesics are a natural model for surfaces made from wood strips. We outline how to construct all solutions, and produce non-trivial examples, such as a wood-strip Klein bottle...

  15. Polyaffine parametrization of image registration based on geodesic flows

    DEFF Research Database (Denmark)

    Hansen, Michael Sass; Thorup, Signe Strann; Warfield, Simon K.

    2012-01-01

    Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which ...... of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether....

  16. On some Closed Magnetic Curves on a 3-torus

    Energy Technology Data Exchange (ETDEWEB)

    Munteanu, Marian Ioan, E-mail: marian.ioan.munteanu@gmail.com [Alexandru Ioan Cuza University of Iaşi, Faculty of Mathematics (Romania); Nistor, Ana Irina, E-mail: ana.irina.nistor@gmail.com [Gh. Asachi Technical University of Iaşi, Department of Mathematics and Informatics (Romania)

    2017-06-15

    We consider two magnetic fields on the 3-torus obtained from two different contact forms on the Euclidean 3-space and we study when their corresponding normal magnetic curves are closed. We obtain periodicity conditions analogues to those for the closed geodesics on the torus.

  17. Dual Smarandache Curves of a Timelike Curve lying on Unit dual Lorentzian Sphere

    OpenAIRE

    Kahraman, Tanju; Hüseyin Ugurlu, Hasan

    2016-01-01

    In this paper, we give Darboux approximation for dual Smarandache curves of time like curve on unit dual Lorentzian sphere. Firstly, we define the four types of dual Smarandache curves of a timelike curve lying on dual Lorentzian sphere.

  18. de Sitter relativity in static charts

    Energy Technology Data Exchange (ETDEWEB)

    Cotaescu, Ion I. [West University of Timisoara, Timisoara (Romania)

    2018-02-15

    The relative geodesic motion in static (and spherically symmetric) local charts on the (1 + 3)-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame of a massive particle freely moving on a timelike geodesic. The time dilation and Lorentz contraction are discussed pointing out some notable features of the de Sitter relativity in static charts. (orig.)

  19. Isometries of half supersymmetric time-like solutions in five dimensions

    International Nuclear Information System (INIS)

    Gutowski, J B; Sabra, W A

    2010-01-01

    Spinorial geometry techniques have recently been used to classify all half supersymmetric solutions in gauged five-dimensional supergravity with vector multiplets. In this paper we consider solutions for which at least one of the Killing spinors generates a time-like Killing vector. We obtain coordinate transformations which considerably simplify the solutions, and in a number of cases, we obtain explicitly some additional Killing vectors which were hidden in the original analysis.

  20. Timelike Compton scattering off the neutron and generalized parton distributions

    Energy Technology Data Exchange (ETDEWEB)

    Boer, M.; Guidal, M. [CNRS-IN2P3, Universite Paris-Sud, Institut de Physique Nucleaire d' Orsay, Orsay (France); Vanderhaeghen, M. [Johannes Gutenberg Universitaet, Institut fuer Kernphysik and PRISMA Cluster of Excellence, Mainz (Germany)

    2016-02-15

    We study the exclusive photoproduction of an electron-positron pair on a neutron target in the Jefferson Lab energy domain. The reaction consists of two processes: the Bethe-Heitler and the Timelike Compton Scattering. The latter process provides potentially access to the Generalized Parton Distributions (GPDs) of the nucleon. We calculate all the unpolarized, single- and double-spin observables of the reaction and study their sensitivities to GPDs. (orig.)

  1. A prescribing geodesic curvature problem

    International Nuclear Information System (INIS)

    Chang, K.C.; Liu, J.Q.

    1993-09-01

    Let D be the unit disk and k be a function on S 1 = δD. Find a flat metric which is pointwise conformal to the standard metric and has k as the geodesic curvature of S 1 . A sufficient condition for the existence of such a metric is that the harmonic extension of k in D has saddle points. (author). 11 refs

  2. Noncrossing timelike singularities of irrotational dust collapse

    International Nuclear Information System (INIS)

    Liang, E.P.T.

    1979-01-01

    Known naked singularities in spherical dust collapse are either due to shell-crossing or localized to the central world line. They will probably be destroyed by pressure gradients or blue-shift instabilities. To violate the cosmic censorship hypothesis in a more convincing and general context, collapse solutions with naked singularities that are at least nonshell-crossing and nonlocalized need to be constructed. Some results concerning the probable structure of a class of nonshellcrossing and nonlocalized timelike singularities are reviewed. The cylindrical dust model is considered but this model is not asymptotically flat. To make these noncrossing singularities viable counter examples to the cosmic censorship hypothesis, the occurrence of such singularities in asymptotically flat collapse needs to be demonstrated. (UK)

  3. ISCO and Principal Null Congruences in Extremal Kerr Spacetime

    International Nuclear Information System (INIS)

    Pradhan, Parthapratim

    2012-01-01

    The effective potential in universal like coordinates(U, V, θ, φ), which are smooth across the event horizon is derived and investigated the ISCO(Innermost Stable Circular Orbits) explicitly in these coordinates for extremal Kerr spacetime. Extremization of the effective potential for timelike circular orbit shows that the existence of a stable circular geodesics in the extremal spacetime for direct orbit, precisely on the event horizon in terms of the radial coordinate which coincides with the principal null geodesic congruences of the event horizon. These null geodesic congruences mold themselves to the spacetime curvature in such a way that Weyl conformal tensor and its dual are vanished, that is why they are in-fact doubly degenerate principal null congruences.

  4. NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface

    DEFF Research Database (Denmark)

    Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole

    2011-01-01

    that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE......An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant......-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine...

  5. NNLO splitting and coefficient functions with time-like kinematics

    International Nuclear Information System (INIS)

    Mitov, A.; Moch, S.; Vogt, A.; Liverpool Univ.

    2006-09-01

    We discuss recent results on the three-loop (next-to-next-to-leading order, NNLO) time-like splitting functions of QCD and the two-loop (NNLO) coefficient functions in one-particle inclusive e + e - -annihilation. These results form the basis for extracting fragmentation functions for light and heavy flavors with NNLO accuracy that will be needed at the LHC and ILC. The two-loop calculations have been performed in Mellin space bases on a new method, the main features of which we also describe briefly. (orig.)

  6. On Geodesic Exponential Kernels

    DEFF Research Database (Denmark)

    Feragen, Aasa; Lauze, François; Hauberg, Søren

    2015-01-01

    This extended abstract summarizes work presented at CVPR 2015 [1]. Standard statistics and machine learning tools require input data residing in a Euclidean space. However, many types of data are more faithfully represented in general nonlinear metric spaces or Riemannian manifolds, e.g. shapes, ......, symmetric positive definite matrices, human poses or graphs. The underlying metric space captures domain specific knowledge, e.g. non-linear constraints, which is available a priori. The intrinsic geodesic metric encodes this knowledge, often leading to improved statistical models....

  7. Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

    Directory of Open Access Journals (Sweden)

    Kun-Lin Wu

    2016-01-01

    Full Text Available In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.

  8. Geodesic structure of Lifshitz black holes in 2+1 dimensions

    International Nuclear Information System (INIS)

    Cruz, Norman; Olivares, Marco; Villanueva, J.R.

    2013-01-01

    We present a study of the geodesic equations of a black hole space-time which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with z=3 and d=1 as found in Ayon-Beato et al. (Phys. Rev. D 80:104029, 2009). By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non-radial geodesics are given in terms of the Weierstrass elliptic p, σ, and ζ functions. (orig.)

  9. Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri's equation

    OpenAIRE

    Rahmani, Faramarz; Golshani, Mehdi

    2017-01-01

    One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since, the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the ...

  10. Timelike Completeness as an Obstruction to C 0-Extensions

    Science.gov (United States)

    Galloway, Gregory J.; Ling, Eric; Sbierski, Jan

    2017-11-01

    The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike complete and globally hyperbolic Lorentzian manifold is C 0-inextendible. For the proof we make use of the result, recently established by Sämann (Ann Henri Poincaré 17(6):1429-1455, 2016), that even for continuous Lorentzian manifolds that are globally hyperbolic, there exists a length-maximizing causal curve between any two causally related points.

  11. Integrability of geodesics and action-angle variables in Sasaki-Einstein space T{sup 1,1}

    Energy Technology Data Exchange (ETDEWEB)

    Visinescu, Mihai [National Institute of Physics and Nuclear Engineering, Department Theoretical Physics, Magurele, Bucharest (Romania)

    2016-09-15

    We briefly describe the construction of Staekel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T{sup 1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed. (orig.)

  12. Null geodesics and embedding diagrams of the interior Schwarzschild--de Sitter spacetimes with uniform density

    International Nuclear Information System (INIS)

    Stuchlik, Zdenek; Hledik, Stanislav; Soltes, Jiri; Ostgaard, Erlend

    2001-01-01

    Null geodesics and embedding diagrams of central planes in the ordinary space geometry and the optical reference geometry of the interior Schwarzschild--de Sitter spacetimes with uniform density are studied. For completeness, both positive and negative values of the cosmological constant are considered. The null geodesics are restricted to the central planes of these spacetimes, and their properties can be reflected by an 'effective potential.' If the interior spacetime is extremely compact, the effective potential has a local maximum corresponding to a stable circular null geodesic around which bound null geodesics are concentrated. The upper limit on the size of the interior spacetimes containing bound null geodesics is R=3M, independently of the value of the cosmological constant. The embedding diagrams of the central planes of the ordinary geometry into three-dimensional Euclidean space are well defined for the complete interior of all spacetimes with a repulsive cosmological constant, but the planes cannot be embedded into the Euclidean space in the case of spacetimes with subcritical values of an attractive cosmological constant. On the other hand, the embedding diagrams of the optical geometry are well defined for all of the spacetimes, and the turning points of these diagrams correspond to the radii of the circular null geodesics. All the embedding diagrams, for both the ordinary and optical geometry, are smoothly matched to the corresponding embedding diagrams of the external vacuum Schwarzschild--de Sitter spacetimes

  13. Revisiting scalar geodesic synchrotron radiation in Kerr spacetime

    International Nuclear Information System (INIS)

    Macedo, Caio F.B.; Crispino, Luis C.B.

    2011-01-01

    Full text: The Kerr solution [R. P. Kerr, Phys. Rev. D 11, 5 (1963)] is one of the most important black hole solutions of Einstein equations. It describes a chargeless rotating black hole, with Schwarzschild black hole as a particular case. It is estimated, inferred using distinct methods, that most black hole candidates have a considerable value of the rotation parameter [E. Berti, V. Cardoso, and A. Starinets, Classical Quantum Gravity 26, 163001 (2009)]. Although the Schwarzschild solution is suitable for a great variety of phenomena in star and black hole physics, the Kerr solution becomes very important in the explanation of the electrodynamical aspects of accretion disks for binary X-ray sources [The Kerr Spacetime: Rotating Black Holes in General Relativity, edited by D. L. Wiltshire, M. Visser, and S. M. Scott (Cambridge University Press, Cambridge, 2009)]. Thus, the investigation of how radiation emission processes are modified by the nontrivial curvature of rotating black holes is particularly important. As a first approximation to the problem, one can consider a moving particle, minimally coupled to the massless scalar field, in circular geodesic motion. The radiation emitted in this configuration is called scalar geodesic synchrotron radiation. In this work, we revisit the main aspects of scalar geodesic synchrotron radiation in Kerr spacetime, including some effects occurring in the high-frequency approximation. Our results can be readily compared with the results of the equivalent phenomena in Schwarzschild spacetime. (author)

  14. On timelike supersymmetric solutions of gauged minimal 5-dimensional supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Chimento, Samuele; Ortín, Tomás [Instituto de Física Teórica UAM/CSIC,C/Nicolás Cabrera, 13-15, C.University Cantoblanco, E-28049 Madrid (Spain)

    2017-04-04

    We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for the case in which the Kähler base manifold admits a holomorphic isometry and depends on two real functions satisfying a simple second-order differential equation. Using this general form of the base space, the equations satisfied by the building blocks of the solutions become of, at most, fourth degree and can be solved by simple polynomic ansatzs. In this way we construct two 3-parameter families of solutions that contain almost all the timelike supersymmetric solutions of this theory with one angular momentum known so far and a few more: the (singular) supersymmetric Reissner-Nordström-AdS solutions, the three exact supersymmetric solutions describing the three near-horizon geometries found by Gutowski and Reall, three 1-parameter asymptotically-AdS{sub 5} black-hole solutions with those three near-horizon geometries (Gutowski and Reall’s black hole being one of them), three generalizations of the Gödel universe and a few potentially homogenous solutions. A key rôle in finding these solutions is played by our ability to write AdS{sub 5}’s Kähler base space ( (ℂℙ)-bar {sup 2} or SU(1,2)/U(2)) is three different, yet simple, forms associated to three different isometries. Furthermore, our ansatz for the Kähler metric also allows us to study the dimensional compactification of the theory and its solutions in a systematic way.

  15. Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory

    International Nuclear Information System (INIS)

    Villanueva, J. R.; Olivares, Marco

    2015-01-01

    Properties of the motion of electrically charged particles in the background of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole is presented in this paper. Radial and angular motions are studied analytically for different values of the fundamental parameter. Therefore, gravitational Rutherford scattering and Keplerian orbits are analyzed in detail. Finally, this paper complements previous work by Fernando for null geodesics (Phys Rev D 85:024033, 2012), Olivares and Villanueva (Eur Phys J C 73:2659, 2013) and Blaga (Automat Comp Appl Math 22:41–48, 2013; Serb Astron 190:41, 2015) for time-like geodesics

  16. Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory

    Energy Technology Data Exchange (ETDEWEB)

    Villanueva, J.R. [Universidad de Valparaiso, Instituto de Fisica y Astronomia, Valparaiso (Chile); Centro de Astrofisica de Valparaiso, Valparaiso (Chile); Olivares, Marco [Universidad Diego Portales, Avenida Ejercito Libertador 441, Facultad de Ingenieria, Santiago (Chile)

    2015-11-15

    Properties of the motion of electrically charged particles in the background of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole is presented in this paper. Radial and angular motions are studied analytically for different values of the fundamental parameter. Therefore, gravitational Rutherford scattering and Keplerian orbits are analyzed in detail. Finally, this paper complements previous work by Fernando for null geodesics (Phys Rev D 85:024033, 2012), Olivares and Villanueva (Eur Phys J C 73:2659, 2013) and Blaga (Automat Comp Appl Math 22:41-48, 2013; Serb Astron 190:41, 2015) for time-like geodesics. (orig.)

  17. Newtonian potential and geodesic completeness in infinite derivative gravity

    Science.gov (United States)

    Edholm, James; Conroy, Aindriú

    2017-08-01

    Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

  18. Adaptive geodesic transform for segmentation of vertebrae on CT images

    Science.gov (United States)

    Gaonkar, Bilwaj; Shu, Liao; Hermosillo, Gerardo; Zhan, Yiqiang

    2014-03-01

    Vertebral segmentation is a critical first step in any quantitative evaluation of vertebral pathology using CT images. This is especially challenging because bone marrow tissue has the same intensity profile as the muscle surrounding the bone. Thus simple methods such as thresholding or adaptive k-means fail to accurately segment vertebrae. While several other algorithms such as level sets may be used for segmentation any algorithm that is clinically deployable has to work in under a few seconds. To address these dual challenges we present here, a new algorithm based on the geodesic distance transform that is capable of segmenting the spinal vertebrae in under one second. To achieve this we extend the theory of the geodesic distance transforms proposed in1 to incorporate high level anatomical knowledge through adaptive weighting of image gradients. Such knowledge may be provided by the user directly or may be automatically generated by another algorithm. We incorporate information 'learnt' using a previously published machine learning algorithm2 to segment the L1 to L5 vertebrae. While we present a particular application here, the adaptive geodesic transform is a generic concept which can be applied to segmentation of other organs as well.

  19. Lagrangian averaging with geodesic mean.

    Science.gov (United States)

    Oliver, Marcel

    2017-11-01

    This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

  20. Null geodesics in black hole metrics with non-zero cosmological constant

    International Nuclear Information System (INIS)

    Stuchlik, Z.; Calvani, M.

    1990-02-01

    We study the radial motion along null geodesics in the Reissner-Nordstroem-de Sitter and Kerr-de Sitter space-times. We analyze the properties of the effective potential and we discuss circular orbits. We find that the radii of circular geodesics in the Reissner-Nordstroem-de Sitter space-time do not depend on the cosmological constant, and we explain this property using the optical reference geometry. In addition, we describe the unusual consequences of the interplay between rotation of the source and cosmological repulsion. (author). 16 refs, 8 figs

  1. Can geodesics in extra dimensions solve the cosmological horizon problem?

    International Nuclear Information System (INIS)

    Chung, Daniel J. H.; Freese, Katherine

    2000-01-01

    We demonstrate a non-inflationary solution to the cosmological horizon problem in scenarios in which our observable universe is confined to three spatial dimensions (a three-brane) embedded in a higher dimensional space. A signal traveling along an extra-dimensional null geodesic may leave our three-brane, travel into the extra dimensions, and subsequently return to a different place on our three-brane in a shorter time than the time a signal confined to our three-brane would take. Hence, these geodesics may connect distant points which would otherwise be ''outside'' the four dimensional horizon (points not in causal contact with one another). (c) 2000 The American Physical Society

  2. Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

    Directory of Open Access Journals (Sweden)

    Panou G.

    2017-02-01

    Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

  3. Optics of relativistic sources in a spherically symmetric gravitational field

    International Nuclear Information System (INIS)

    Campbell, G.A.

    1975-01-01

    The effects of spectral shifts and gravitational focussing on radiation from sources moving geodesically in the Schwarzschild gravitational field is analyzed using the general-relativistic equations for geodesic motion and for the propagation of radiation along null geodesics in the geometrical optics approximation. The exact solutions of the Schwarzschild geodesic equations are briefly discussed for the null and time-like cases, and the method of classifying the orbital types of motion based on the effective radial potential is presented. A method of finding the stability of these orbits using this technique is discussed. The geometrical optics approximation for the propagation of radiation is discussed, and the area-intensity law for the Schwarzschild field is derived. The particularly interesting region near R = 3m is investigated by means of expansions of the exact equations. Numerical techniques for calculating radiation patterns from the propagation equations are discussed, including techniques for obtaining the time variation along geodesics and differences in propagation time along different null geodesics. Finally, the implications of these calculations for the apparent contradiction in energy requirements set by Joseph Weber's observations of galactic gravitational radiation and by astronomical observation are discussed. (Diss. Abstr. Int., B)

  4. Fermions on spacetimes of spatially closed hypersurfaces

    International Nuclear Information System (INIS)

    Dariescu, Marina-Aura; Dariescu, Ciprian

    2009-01-01

    Using a convenient compact time-like coordinate f element of [0, 1], characterizing the whole big bang-big crunch spacetime history cyclicly evolving with a 2π conformal period, we write down the Dirac-type equation in a FRW matter-dominated Universe. It turns out that, by accepting the idea of existence of an alternative time gauge, as for example in the projected Universe, one is able to derive closed form solutions, for physically meaningful cases.

  5. On geodesics with negative energies in the ergoregions of dirty black holes

    Science.gov (United States)

    Zaslavskii, O. B.

    2015-03-01

    We consider behavior of equatorial geodesics with the negative energy in the ergoregion of a generic rotating "dirty" (surrounded by matter) black hole. It is shown that under very simple and generic conditions on the metric coefficients, there are no such circular orbits. This entails that such geodesic must originate and terminate under the event horizon. These results generalize the observation made for the Kerr metric in A. A. Grib, Yu. V. Pavlov and V. D. Vertogradov, Mod. Phys. Lett.29, 1450110 (2014), arXiv:1304.7360.

  6. Properties of an Arithmetic Code for Geodesic Flows

    International Nuclear Information System (INIS)

    Chaves, Daniel P B; Palazzo, Reginaldo Jr; Rios Leite, Jose R

    2011-01-01

    Topological analysis of chaotic dynamical systems emerged in the nineties as a powerful tool in the study of strange attractors in low-dimensional dynamical systems. It is based on identifying the stretching and squeezing mechanisms responsible for creating a strange attractor and organize all the unstable periodic orbits in this attractor. This method is concerned with the manifold generated by the chaotic system. Furthermore, as a mathematical object, the manifolds have a well studied geometric and algebraic structure, particularly for the case of compact surfaces. Intending to use this structure in the analysis and application of chaotic systems through their topological characteristics, we determine properties of geodesic codes for compact surfaces necessary for the construction of encoders from the symbolic sequences of experimental data generated by the unstable periodic orbits of the strange attractor (related to the behavior changes of the system with the variation of control parameters) to the geodesic code sequences, which permits to use the surface structure to study the system orbits.

  7. Unique Two-Way Field Probe Concept Utilizing a Geodesic Sphere and Quad-Rotor

    Science.gov (United States)

    2015-03-26

    encompass the quad-rotor. This cage will behave like a faraday cage of sorts, shielding the quad-rotor’s RCS phenomenology from the radar’s antenna...test volume. Second, because the quad-rotor’s structural geometry is a cause for concern, a geodesic cage , in the shape of a sphere, will be built to...be the development of the geodesic cage that will encompass the quad-rotor along with an analysis of its scattering statistics as function of the

  8. Black hole decay as geodesic motion

    International Nuclear Information System (INIS)

    Gupta, Kumar S.; Sen, Siddhartha

    2003-01-01

    We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach predicts a precise correction term to the usual expression for the decay rate of black holes

  9. Perfect fluid cosmology with geodesic world lines

    International Nuclear Information System (INIS)

    Raychaudhuri, A.K.; Maity, S.R.

    1978-01-01

    It is shown that for a perfect fluid with an equation of state p = p (rho), if the world lines are geodesics, then they are hypersurface orthogonal and the scalars p, rho, sigma 2 , and theta 2 are all constants over these hypersurfaces, irrespective of any spatial-homogeneity assumption. However, an examination of some simple cases does not reveal any spatially nonhomogeneous solution with these properties

  10. Pulmonary parenchyma segmentation in thin CT image sequences with spectral clustering and geodesic active contour model based on similarity

    Science.gov (United States)

    He, Nana; Zhang, Xiaolong; Zhao, Juanjuan; Zhao, Huilan; Qiang, Yan

    2017-07-01

    While the popular thin layer scanning technology of spiral CT has helped to improve diagnoses of lung diseases, the large volumes of scanning images produced by the technology also dramatically increase the load of physicians in lesion detection. Computer-aided diagnosis techniques like lesions segmentation in thin CT sequences have been developed to address this issue, but it remains a challenge to achieve high segmentation efficiency and accuracy without much involvement of human manual intervention. In this paper, we present our research on automated segmentation of lung parenchyma with an improved geodesic active contour model that is geodesic active contour model based on similarity (GACBS). Combining spectral clustering algorithm based on Nystrom (SCN) with GACBS, this algorithm first extracts key image slices, then uses these slices to generate an initial contour of pulmonary parenchyma of un-segmented slices with an interpolation algorithm, and finally segments lung parenchyma of un-segmented slices. Experimental results show that the segmentation results generated by our method are close to what manual segmentation can produce, with an average volume overlap ratio of 91.48%.

  11. Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions

    Energy Technology Data Exchange (ETDEWEB)

    Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)

    2009-12-31

    A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.

  12. Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation

    Science.gov (United States)

    Rahmani, Faramarz; Golshani, Mehdi

    2018-01-01

    One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space-time metric.

  13. FLAT TIME-LIKE SUBMANIFOLDS IN ANTI-DE SITTER SPACE H12n-1(-1)

    Institute of Scientific and Technical Information of China (English)

    ZUO DAFENG; CHEN QING; CHENG YI

    2005-01-01

    By using dressing actions of the Gn-1 1,1,n-1-system, the authors study geometric transformations for flat time-like n-submanifolds with flat, non-degenerate normal bun dle in anti-de Sitter space H1 2n-1(-1), where G1,1 n-1,n-1= O(2n - 2, 2)/O(n - 1, 1) ×O(n - 1, 1).

  14. MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

    Energy Technology Data Exchange (ETDEWEB)

    Florinski, V. [Department of Physics, University of Alabama, Huntsville, AL 35899 (United States); Guo, X. [Center for Space Plasma and Aeronomic Research, University of Alabama, Huntsville, AL 35899 (United States); Balsara, D. S.; Meyer, C. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States)

    2013-04-01

    This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

  15. MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

    International Nuclear Information System (INIS)

    Florinski, V.; Guo, X.; Balsara, D. S.; Meyer, C.

    2013-01-01

    This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

  16. Kinematic space and wormholes

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Jian-dong [TianQin Research Center for Gravitational Physics, Sun Yat-sen University, Zhuhai 519082, Guangdong (China); Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter, 5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University, 5 Yiheyuan Rd, Beijing 100871 (China)

    2017-01-23

    The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic space could be intrinsically defined in the embedding space. For each oriented geodesic in the Poincaré disk, there is a corresponding point in the kinematic space. This point is the tip of the causal diamond of the disk whose intersection with the Poincaré disk determines the geodesic. In this geometric construction, the causal structure in the kinematic space can be seen clearly. Moreover, we find that every transformation in the SL(2,ℝ) leads to a geodesic in the kinematic space. In particular, for a hyperbolic transformation defining a BTZ black hole, it is a timelike geodesic in the kinematic space. We show that the horizon length of the static BTZ black hole could be computed by the geodesic length of corresponding points in the kinematic space. Furthermore, we discuss the fundamental regions in the kinematic space for the BTZ blackhole and multi-boundary wormholes.

  17. Exact relativistic cylindrical solution of disordered radiation

    International Nuclear Information System (INIS)

    Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.

    1976-05-01

    A source free disordered distribution of electromagnetic radiation is considered in Einstein' theory, and a time independent exact solution with cylindrical symmetry is obtained. The gravitation and pressure effects of the radiation alone are sufficient to give the distribution an equilibrium. A finite maximum concentration is found on the axis of symmetry, and decreases monotonically to zero outwards. Timelike and null geodesics are discussed

  18. Geodesic atlas-based labeling of anatomical trees

    DEFF Research Database (Denmark)

    Feragen, Aasa; Petersen, Jens; Owen, Megan

    2015-01-01

    We present a fast and robust atlas-based algorithm for labeling airway trees, using geodesic distances in a geometric tree-space. Possible branch label configurations for an unlabeled airway tree are evaluated using distances to a training set of labeled airway trees. In tree-space, airway tree t...... equally complete airway trees, and comparable in performance to that of experts in pulmonary medicine, emphasizing the suitability of the labeling algorithm for clinical use....

  19. Asymptotically AdS spacetimes with a timelike Kasner singularity

    Energy Technology Data Exchange (ETDEWEB)

    Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)

    2016-07-21

    Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.

  20. Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

    Science.gov (United States)

    Deng, Gao-Ming; Huang, Yong-Chang

    2018-03-01

    The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.

  1. One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance

    Science.gov (United States)

    Fröb, Markus B.

    2018-02-01

    We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and strongly divergent, and we show how to renormalise them by performing a ‘wave function renormalisation’ of the geodesic embedding coordinates. The result is finite and gauge-independent, but displays unusual features such as double logarithms at one-loop order.

  2. Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion

    Science.gov (United States)

    Barack, Leor

    The question of motion in a gravitationally bound two-body system is a longstanding open problem of General Relativity. When the mass ratio eta; is small, the problem lends itself to a perturbative treatment, wherein corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in η, using the language of an effective gravitational self-force. The prospect for observing gravitational waves from compact objects inspiralling into massive black holes in the foreseeable future has in the past 15 years motivated a program to obtain a rigorous formulation of the self-force and compute it for astrophysically interesting systems. I will give a brief survey of this activity and its achievements so far, and will identify the challenges that lie ahead. As concrete examples, I will discuss recent calculations of certain conservative post-geodesic effects of the self-force, including the O(η ) correction to the precession rate of the periastron. I will highlight the way in which such calculations allow us to make a fruitful contact with other approaches to the two-body problem.

  3. Geodesics on a hot plate: an example of a two-dimensional curved space

    International Nuclear Information System (INIS)

    Erkal, Cahit

    2006-01-01

    The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion

  4. Geodesics on a hot plate: an example of a two-dimensional curved space

    Energy Technology Data Exchange (ETDEWEB)

    Erkal, Cahit [Department of Geology, Geography, and Physics, University of Tennessee, Martin, TN 38238 (United States)

    2006-07-01

    The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion.

  5. Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves

    Science.gov (United States)

    Heydari-Fard, M.; Hasani, S. N.

    We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R. Colistete Jr., Class. Quantum Grav. 18 (2001) 4725]. By solving these equations for charged particles moving in a constant magnetic field in the spacetime of a gravitational wave, we show for both cases when the gravitational wave is parallel and perpendicular to the constant magnetic field, a magnetic resonance appears at wg = Ω. This feature might be useful to detect the gravitational wave with high frequencies.

  6. On the Robinson theorem and shearfree geodesic null congruences

    International Nuclear Information System (INIS)

    Tafel, J.

    1985-01-01

    Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions. (orig.)

  7. Conventional Gymnasium vs. Geodesic Field House. A Comparative Study of High School Physical Education and Assembly Facilities.

    Science.gov (United States)

    Educational Facilities Labs., Inc., New York, NY.

    A description is presented of the design features of a high school's geodesic dome field house. Following consideration of various design features and criteria for the physical education facility, a comprehensive analysis is given of comparative costs of a geodesic dome field house and conventional gymnasium. On the basis of the study it would…

  8. New perspectives for high accuracy SLR with second generation geodesic satellites

    Science.gov (United States)

    Lund, Glenn

    1993-01-01

    This paper reports on the accuracy limitations imposed by geodesic satellite signatures, and on the potential for achieving millimetric performances by means of alternative satellite concepts and an optimized 2-color system tradeoff. Long distance laser ranging, when performed between a ground (emitter/receiver) station and a distant geodesic satellite, is now reputed to enable short arc trajectory determinations to be achieved with an accuracy of 1 to 2 centimeters. This state-of-the-art accuracy is limited principally by the uncertainties inherent to single-color atmospheric path length correction. Motivated by the study of phenomena such as postglacial rebound, and the detailed analysis of small-scale volcanic and strain deformations, the drive towards millimetric accuracies will inevitably be felt. With the advent of short pulse (less than 50 ps) dual wavelength ranging, combined with adequate detection equipment (such as a fast-scanning streak camera or ultra-fast solid-state detectors) the atmospheric uncertainty could potentially be reduced to the level of a few millimeters, thus, exposing other less significant error contributions, of which by far the most significant will then be the morphology of the retroreflector satellites themselves. Existing geodesic satellites are simply dense spheres, several 10's of cm in diameter, encrusted with a large number (426 in the case of LAGEOS) of small cube-corner reflectors. A single incident pulse, thus, results in a significant number of randomly phased, quasi-simultaneous return pulses. These combine coherently at the receiver to produce a convolved interference waveform which cannot, on a shot to shot basis, be accurately and unambiguously correlated to the satellite center of mass. This paper proposes alternative geodesic satellite concepts, based on the use of a very small number of cube-corner retroreflectors, in which the above difficulties are eliminated while ensuring, for a given emitted pulse, the return

  9. Geodesic least squares regression for scaling studies in magnetic confinement fusion

    International Nuclear Information System (INIS)

    Verdoolaege, Geert

    2015-01-01

    In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices

  10. Ergodic Properties of the Quantum Geodesic Flow on Tori

    Energy Technology Data Exchange (ETDEWEB)

    Klimek, SLawomir [Indiana University Purdue University Indianapolis, Department of Mathematics (United States); Kondracki, Witold [Polish Academy of Sciences, Institute of Mathematics (Poland)

    2005-05-15

    We study ergodic averages for a class of pseudo-differential operators on the flat N-dimensional torus with respect to the Schroedinger evolution. The later can be consider a quantization of the geodesic flow on T{sup N}. We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.

  11. A comment on the null geodesic equations in Schwarzschild geometry

    International Nuclear Information System (INIS)

    Rosa, M.A.F.; Rodrigues Junior, W.A.

    1986-01-01

    An integration of the null geodesic equations in the Schwarzschild geometry, which is valid to first order in GM/Rc 2 is presented. The solution is compared with others published in the literature and their range of validity is analysed. Some misunderstandings are also clarified. (Author) [pt

  12. Null geodesics and wave front singularities in the Gödel space-time

    Science.gov (United States)

    Kling, Thomas P.; Roebuck, Kevin; Grotzke, Eric

    2018-01-01

    We explore wave fronts of null geodesics in the Gödel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Gödel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.

  13. AdS/CFT prescription for angle-deficit space and winding geodesics

    International Nuclear Information System (INIS)

    Aref’eva, Irina Ya.; Khramtsov, Mikhail A.

    2016-01-01

    We present the holographic computation of the boundary two-point correlator using the GKPW prescription for a scalar field in the AdS_3 space with a conical defect. Generally speaking, a conical defect breaks conformal invariance in the dual theory, however we calculate the classical bulk-boundary propagator for a scalar field in the space with conical defect and use it to compute the two-point correlator in the boundary theory. We compare the obtained general expression with previous studies based on the geodesic approximation. They are in good agreement for short correlators, and main discrepancy comes in the region of long correlations. Meanwhile, in case of ℤ_r-orbifold, the GKPW result coincides with the one obtained via geodesic images prescription and with the general result for the boundary theory, which is conformal in this special case.

  14. Investigation of energetic particle induced geodesic acoustic mode

    Science.gov (United States)

    Schneller, Mirjam; Fu, Guoyong; Chavdarovski, Ilija; Wang, Weixing; Lauber, Philipp; Lu, Zhixin

    2017-10-01

    Energetic particles are ubiquitous in present and future tokamaks due to heating systems and fusion reactions. Anisotropy in the distribution function of the energetic particle population is able to excite oscillations from the continuous spectrum of geodesic acoustic modes (GAMs), which cannot be driven by plasma pressure gradients due to their toroidally and nearly poloidally symmetric structures. These oscillations are known as energetic particle-induced geodesic acoustic modes (EGAMs) [G.Y. Fu'08] and have been observed in recent experiments [R. Nazikian'08]. EGAMs are particularly attractive in the framework of turbulence regulation, since they lead to an oscillatory radial electric shear which can potentially saturate the turbulence. For the presented work, the nonlinear gyrokinetic, electrostatic, particle-in-cell code GTS [W.X. Wang'06] has been extended to include an energetic particle population following either bump-on-tail Maxwellian or slowing-down [Stix'76] distribution function. With this new tool, we study growth rate, frequency and mode structure of the EGAM in an ASDEX Upgrade-like scenario. A detailed understanding of EGAM excitation reveals essential for future studies of EGAM interaction with micro-turbulence. Funded by the Max Planck Princeton Research Center. Computational resources of MPCDF and NERSC are greatefully acknowledged.

  15. From Geodesic Flow on a Surface of Negative Curvature to Electronic Generator of Robust Chaos

    Science.gov (United States)

    Kuznetsov, Sergey P.

    2016-12-01

    Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependencies of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow.

  16. Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency

    Energy Technology Data Exchange (ETDEWEB)

    Lakhin, V.P. [NRC “Kurchatov Institute”, Moscow (Russian Federation); Sorokina, E.A., E-mail: sorokina.ekaterina@gmail.com [NRC “Kurchatov Institute”, Moscow (Russian Federation); Peoples' Friendship University of Russia, Moscow (Russian Federation)

    2014-01-24

    The geodesic acoustic eigenmode for tokamak equilibrium with the maximum of local GAM frequency is found analytically in the frame of MHD model. The analysis is based on the asymptotic matching technique.

  17. The topology of geodesically complete space-times

    International Nuclear Information System (INIS)

    Lee, C.W.

    1983-01-01

    Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic to S 3 then the part of space-time that it encloses must be simply connected. (author)

  18. Quantum correlator outside a Schwarzschild black hole

    Directory of Open Access Journals (Sweden)

    Claudia Buss

    2018-01-01

    Full Text Available We calculate the quantum correlator in Schwarzschild black hole space–time. We perform the calculation for a scalar field in three different quantum states: Boulware, Unruh and Hartle–Hawking, and for points along a timelike circular geodesic. The results show that the correlator presents a global fourfold singularity structure, which is state-independent. Our results also show the different correlations in the three different quantum states arising in-between the singularities.

  19. A Finsler geodesic spray paradigm for wildfire spread modelling

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2015-01-01

    represents the local fire templates. The ‘paradigm’ part of the present proposal is thus concerned with the corresponding shift of attention from the actual fire-lines to consider instead the geodesic spray - the ‘fire-particles’ - which together, side by side, mold the fire-lines at each instant of time...... and thence eventually constitute the local and global structure of the wildfire spread....

  20. The inherent dynamics of a molecular liquid: Geodesic pathways through the potential energy landscape of a liquid of linear molecules

    Science.gov (United States)

    Jacobson, Daniel; Stratt, Richard M.

    2014-05-01

    Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation—molecules largely thread their way through narrow channels available in the potential energy landscape.

  1. An exact Jacobi map in the geodesic light-cone gauge

    CERN Document Server

    Fanizza, G.; Marozzi, G.; Veneziano, G.

    2013-11-07

    The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodetic-deviation equation, and thus to derive an exact expression for the Jacobi map J^A_B(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J^A_B factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J^A_B is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on l...

  2. The full integration of black hole solutions to symmetric supergravity theories

    Energy Technology Data Exchange (ETDEWEB)

    Chemissany, W., E-mail: wissam.chemissany@uleth.c [University of Lethbridge, Physics Department, Lethbridge Alberta, T1K 3M4 (Canada); Rosseel, J., E-mail: rosseel@to.infn.i [Dipartimento di Fisica Teorica, Universita di Torino and INFN-Sezione di Torino, Via P. Giuria 1, I-10125 Torino (Italy); Trigiante, M., E-mail: mario.trigiante@polito.i [Dipartimento di Fisica Politecnico di Torino, C.so Duca degli Abruzzi, 24, I-10129 Torino (Italy); Van Riet, T., E-mail: thomas.vanriet@fysast.uu.s [Institutionen foer Fysik och Astronomi, Box 803, SE-751 08 Uppsala (Sweden)

    2010-05-11

    We prove that all stationary and spherical symmetric black hole solutions to theories with symmetric target spaces are integrable and we provide an explicit integration method. This exact integration is based on the description of black hole solutions as geodesic curves on the moduli space of the theory when reduced over the time-like direction. These geodesic equations of motion can be rewritten as a specific Lax pair equation for which mathematicians have provided the integration algorithms when the initial conditions are described by a diagonalizable Lax matrix. On the other hand, solutions described by nilpotent Lax matrices, which originate from extremal regular (small) D=4 black holes can be obtained as suitable limits of solutions obtained in the diagonalizable case, as we show on the generating geodesic (i.e. most general geodesic modulo global symmetries of the D=3 model) corresponding to regular (and small) D=4 black holes. As a byproduct of our analysis we give the explicit form of the 'Wick rotation' connecting the orbits of BPS and non-BPS solutions in maximally supersymmetric supergravity and its STU truncation.

  3. Do extended objects move along the geodesics in the Riemann space-time

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.

    1981-01-01

    Movement of an extended self-gravitating body in the gravitational field of another distant body is studied in the postnewtonian approximation of arbitrary metrical gravitational theory. Comparison of the mass center acceleration of the extended body with the acceleration of a point body moving in the Riemann space-time, the metrics of which is formally equivalent to the metrics of two moving extended bodies, shows that in any metrical gravitation theory with conservation laws of energy and momentum of the matter and gravitational field taken together, the mass center of the extended body does not, in general case, move along the geodesics of the Riemann space-time. Application of the general formulas obtained to the system Sun-Earth combined with the experimental data of the lunar laser ranging, shows that the Earth in its orbital motion is oscillating with respect to reference geodesics, with the period about one hour and the amplitude not less than 10 -2 cm. This amplitude is of the postnewtonian magnitude and as a consequence, the deviation of the Earth movement from the geodesical movement can be observed in the experiment possessing the postnewtonian accuracy. The difference between the acceleration of the Earth mass center and that of a test body in the postnewtonian approximation is equal to 10 -7 part of the Earth acceleration. The ratio of the passive gravitational mass of the Earth (defined according to Will) and its inert mass differs from 1 by 10 -8 approximately [ru

  4. Conformal gravity, the Einstein equations and spaces of complex null geodesics

    Energy Technology Data Exchange (ETDEWEB)

    Baston, R.J.; Mason, L.J.

    1987-07-01

    The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved.

  5. Conformal gravity, the Einstein equations and spaces of complex null geodesics

    International Nuclear Information System (INIS)

    Baston, R.J.; Mason, L.J.

    1987-01-01

    The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved. (author)

  6. Geodesics of black holes with dark energy

    Science.gov (United States)

    Ghaderi, K.

    2017-12-01

    Dark energy is the most popular hypothesis to explain recent observations suggesting that the world will increasingly expand. One of the models of dark energy is quintessence which is highly plausible. In this paper, we investigate the effect of dark energy on the null geodesics of Schwarzschild, Reissner-Nordström, Schwarzschild-de Sitter and Bardeen black holes. Using the definition of effective potential, the radius of the circular orbits, the period, the instability of the circular orbits, the force exerted on the photons and the deviation angle of light in quintessence field are calculated and the results are analyzed and discussed.

  7. Arcmancer: Geodesics and polarized radiative transfer library

    Science.gov (United States)

    Pihajoki, Pauli; Mannerkoski, Matias; Nättilä, Joonas; Johansson, Peter H.

    2018-05-01

    Arcmancer computes geodesics and performs polarized radiative transfer in user-specified spacetimes. The library supports Riemannian and semi-Riemannian spaces of any dimension and metric; it also supports multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. Arcmancer can be used to solve various problems in numerical geometry, such as solving the curve equation of motion using adaptive integration with configurable tolerances and differential equations along precomputed curves. It also provides support for curves with an arbitrary acceleration term and generic tools for generating ray initial conditions and performing parallel computation over the image, among other tools.

  8. Geodesic curve-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing

    International Nuclear Information System (INIS)

    Saito, Ryo; Naruko, Atsushi; Hiramatsu, Takashi; Sasaki, Misao

    2014-01-01

    In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing

  9. Completely integrable 2D Lagrangian systems and related integrable geodesic flows on various manifolds

    International Nuclear Information System (INIS)

    Yehia, Hamad M

    2013-01-01

    In this study we have formulated a theorem that generates deformations of the natural integrable conservative systems in the plane into integrable systems on Riemannian and other manifolds by introducing additional parameters into their structures. The relation of explicit solutions of the new and the original dynamics to the corresponding Jacobi (Maupertuis) geodesic flow is clarified. For illustration, we apply the result to three concrete examples of the many available integrable systems in the literature. Complementary integrals in those systems are polynomial in velocity with degrees 3, 4 and 6, respectively. As a special case of the first deformed system, a new several-parameter family of integrable mechanical systems (and geodesic flows) on S 2 is constructed. (paper)

  10. Classical resolution of black hole singularities via wormholes

    Energy Technology Data Exchange (ETDEWEB)

    Olmo, Gonzalo J. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Rubiera-Garcia, D. [Universidade de Lisboa, Faculdade de Ciencias, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Sanchez-Puente, A. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain)

    2016-03-15

    In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature. (orig.)

  11. On crossing the Cauchy horizon of a Reissner-Nordstroem black-hole

    International Nuclear Information System (INIS)

    Chandrasekhar, S.; Hartle, J.B.

    1982-01-01

    The behaviour, on the Cauchy horizon, of a flux of gravitational and/or electromagnetic radiation crossing the event horizon of a Reissner-Nordstroem black-hole is investigated as a problem in the theory of one-dimensional potential-scattering. It is shown that the flux of radiation received by an observer crossing the Cauchy horizon, along a radial time-like geodesic, diverges for all physically perturbations crossing the event horizon, even including those with compact support. (author)

  12. Average geodesic distance of skeleton networks of Sierpinski tetrahedron

    Science.gov (United States)

    Yang, Jinjin; Wang, Songjing; Xi, Lifeng; Ye, Yongchao

    2018-04-01

    The average distance is concerned in the research of complex networks and is related to Wiener sum which is a topological invariant in chemical graph theory. In this paper, we study the skeleton networks of the Sierpinski tetrahedron, an important self-similar fractal, and obtain their asymptotic formula for average distances. To provide the formula, we develop some technique named finite patterns of integral of geodesic distance on self-similar measure for the Sierpinski tetrahedron.

  13. Non-relativistic conformal symmetries and Newton-Cartan structures

    International Nuclear Information System (INIS)

    Duval, C; Horvathy, P A

    2009-01-01

    This paper provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational 'dynamical exponent', z. The Schroedinger-Virasoro algebra of Henkel et al corresponds to z = 2. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schroedinger Lie algebra, for which z = 2. For lightlike geodesics, they yield, in turn, the Conformal Galilean Algebra (CGA) of Lukierski, Stichel and Zakrzewski (alias 'alt' of Henkel), with z = 1. Physical systems realizing these symmetries include, e.g. classical systems of massive and massless non-relativistic particles, and also hydrodynamics, as well as Galilean electromagnetism.

  14. Do electromagnetic waves always propagate along null geodesics?

    International Nuclear Information System (INIS)

    Asenjo, Felipe A; Hojman, Sergio A

    2017-01-01

    We find exact solutions to Maxwell equations written in terms of four-vector potentials in non–rotating, as well as in Gödel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled second-order differential equations for combinations of the components of the four-vector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non–rotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on Gödel and Kerr spacetimes do not exhibit that behavior. (paper)

  15. Geodesic acoustic modes in noncircular cross section tokamaks

    Energy Technology Data Exchange (ETDEWEB)

    Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com; Lakhin, V. P. [National Research Center “Kurchatov Institute,” (Russian Federation); Konovaltseva, L. V. [People’s Friendship University of Russia (Russian Federation); Ilgisonis, V. I. [National Research Center “Kurchatov Institute,” (Russian Federation)

    2017-03-15

    The influence of the shape of the plasma cross section on the continuous spectrum of geodesic acoustic modes (GAMs) in a tokamak is analyzed in the framework of the MHD model. An expression for the frequency of a local GAM for a model noncircular cross section plasma equilibrium is derived. Amendments to the oscillation frequency due to the plasma elongation and triangularity and finite tokamak aspect ratio are calculated. It is shown that the main factor affecting the GAM spectrum is the plasma elongation, resulting in a significant decrease in the mode frequency.

  16. Fundamental geodesic deformations in spaces of treelike shapes

    DEFF Research Database (Denmark)

    Feragen, Aasa; Lauze, Francois Bernard; Nielsen, Mads

    2010-01-01

    This paper presents a new geometric framework for analysis of planar treelike shapes for applications such as shape matching, recognition and morphology, using the geometry of the space of treelike shapes. Mathematically, the shape space is given the structure of a stratified set which...... is a quotient of a normed vector space with a metric inherited from the vector space norm. We give examples of geodesic paths in tree-space corresponding to fundamental deformations of small trees, and discuss how these deformations are key building blocks for understanding deformations between larger trees....

  17. A Continuum Mechanical Approach to Geodesics in Shape Space

    Science.gov (United States)

    2010-01-01

    mean curvature flow equation. Calc. Var., 3:253–271, 1995. [30] Siddharth Manay, Daniel Cremers , Byung-Woo Hong, Anthony J. Yezzi, and Stefano Soatto...P. W. Michor and D. Mumford. Riemannian geometries on spaces of plane curves. J. Eur. Math. Soc., 8:1–48, 2006. 37 [33] Peter W. Michor, David ... Cremers . Shape matching by variational computation of geodesics on a manifold. In Pattern Recognition, LNCS 4174, pages 142–151, 2006. [38] P

  18. Goedel-type metrics in various dimensions

    International Nuclear Information System (INIS)

    Guerses, Metin; Karasu, Atalay; Sarioglu, Oezguer

    2005-01-01

    Goedel-type metrics are introduced and used in producing charged dust solutions in various dimensions. The key ingredient is a (D - 1)-dimensional Riemannian geometry which is then employed in constructing solutions to the Einstein-Maxwell field equations with a dust distribution in D dimensions. The only essential field equation in the procedure turns out to be the source-free Maxwell's equation in the relevant background. Similarly the geodesics of this type of metric are described by the Lorentz force equation for a charged particle in the lower dimensional geometry. It is explicitly shown with several examples that Goedel-type metrics can be used in obtaining exact solutions to various supergravity theories and in constructing spacetimes that contain both closed timelike and closed null curves and that contain neither of these. Among the solutions that can be established using non-flat backgrounds, such as the Tangherlini metrics in (D - 1)-dimensions, there exists a class which can be interpreted as describing black-hole-type objects in a Goedel-like universe

  19. Cosmological models in globally geodesic coordinates. II. Near-field approximation

    International Nuclear Information System (INIS)

    Liu Hongya

    1987-01-01

    A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel'dovich, as its near-field approximation in the observer's globally geodesic coordinate system

  20. Do extended bodies move alon.o the geodesics of the Riemannian space-time

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.

    1980-01-01

    Motion of a massive self-gravitating body in the gravitational field of a distant massive source has been considered in the post-Newtonian approximation of the arbitrary metric gravitational theory. The comparison of the massive body center of mass acceleration with that of a point one, moving in Riemannian space-time, whose metrics formally is equivalent to the metrics of two moving massive bodies, makes it clear that in any metric gravitation theory, possessing energy-momentum conservation lows for matter and gravitational field, taken together, massive body does not move generally speaking along the geodesics of Riemannian space-time. Application of the obtained general formulae to the system Earth-Sun and using of the experimental results from lunar-laser-ranging has shown that the Earth during its motion along the orbit, oscillates with respect to the reference geodesic of the geometry with the period of 1 hour and the amplitude not less than 10 -2 cm, which is a post-Newtonian quantity. Therefore the deviation of the Earth motion from the geodesic may be observed in a relevant experiment, which will have a post-Newtonian accuracy. The difference in accelerations of the Earth c.m. and a prob body makes up 10 -7 in the post-Newtonian approximation from the value of the Earth acceleration. The ratio of the passive gravitational mass (defined according to Will) to the inertial mass for the Earth is not equal to unity, and differs from it by the value of approximately 10 -8

  1. Magnetic tension and gravitational collapse

    International Nuclear Information System (INIS)

    Tsagas, Christos G

    2006-01-01

    The gravitational collapse of a magnetized medium is investigated by studying qualitatively the convergence of a timelike family of non-geodesic worldlines in the presence of a magnetic field. Focusing on the field's tension, we illustrate how the winding of the magnetic forcelines due to the fluid's rotation assists the collapse, while shear-like distortions in the distribution of the field's gradients resist contraction. We also show that the relativistic coupling between magnetism and geometry, together with the tension properties of the field, lead to a magneto-curvature stress that opposes the collapse. This tension stress grows stronger with increasing curvature distortion, which means that it could potentially dominate over the gravitational pull of the matter. If this happens, a converging family of non-geodesic worldlines can be prevented from focusing without violating the standard energy conditions

  2. A Time-Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

    Science.gov (United States)

    Vo Van, Thuan

    2017-12-01

    Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time-space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space-time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space-time-matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.

  3. F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements

    Science.gov (United States)

    Karney, C. F. F.; Deakin, R. E.

    2010-08-01

    Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3

  4. Asymptotically shear-free and twist-free null geodesic congruences

    International Nuclear Information System (INIS)

    Kozameh, Carlos; Newman, Ezra T

    2007-01-01

    The Robinson-Trautman spacetime is a special case of asymptotically flat spacetimes that possess asymptotically shear-free and twist-free (surface forming) null geodesic congruences. In this paper we show that, although they are rare, a larger class of asymptotically flat spacetimes with this property does exist. In particular, we display the class of spacetimes that possess this dual property and demonstrate how these congruences can be found. In addition, we show that in each case the congruence is isolated in the sense that there are no other neighbouring congruences with this dual property

  5. Einstein-Rosen 'bridge' revisited and lightlike thin-shell wormholes

    International Nuclear Information System (INIS)

    Guendelman, E.; Nissimov, E.; Pacheva, S.; Stoilov, M.

    2017-01-01

    We study in some detail the properties of the mathematically correct formulation of the classical Einstein-Rosen 'bridge' as proposed in the original 1935 paper, which was shown in a series of previous papers of ours to represent the simplest example of a static spherically symmetric traversable lightlike thin-shell wormhole. Thus, the original Einstein-Rosen 'bridge' is not equivalent to the concept of the dynamical and non-traversable Schwarzschild wormhole, also called 'Einstein-Rosen bridge' in modern textbooks on general relativity. The original Einstein-Rosen 'bridge' requires the presence of a special kind of 'exotic' matter source located on its throat which was shown to be the simplest member of the previously introduced by us class of lightlike membranes. We introduce and exploit the Kruskal-Penrose description of the original Einstein-Rosen 'bridge'. In particular, we explicitly construct closed timelike geodesics on the pertinent Kruskal-Penrose manifold.

  6. Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime

    International Nuclear Information System (INIS)

    Campiglia, Miguel

    2015-01-01

    We elaborate on the Green’s functions that appeared in http://dx.doi.org/10.1007/JHEP07(2015)115http://arxiv.org/abs/1509.01406 when generalizing, from massless to massive particles, various equivalences between soft theorems and Ward identities of large gauge symmetries. We analyze these Green’s functions in considerable detail and show that they form a hierarchy of functions which describe ‘boundary to bulk’ propagators for large U(1) gauge parameters, supertranslations and sphere vector fields respectively. As a consistency check we verify that the Green’s functions associated to the large diffeomorphisms map the Poincare group at null infinity to the Poincare group at time-like infinity.

  7. An equation satisfied by the tangent to a shear-free, geodesic, null congruence

    International Nuclear Information System (INIS)

    Hogan, P.A.; Dublin Inst. for Advanced Studies

    1987-01-01

    A tensorial equation satisfied by the tangent to a shear-free geodesic, null congruence is presented. If the congruence is neither twist-free nor expansion-free then the equation defines a second, unique, null direction previously obtained, using the spinor formalism, by Somers. Some further properties of the equation are discussed. (orig.)

  8. Light-cone averaging in cosmology: formalism and applications

    International Nuclear Information System (INIS)

    Gasperini, M.; Marozzi, G.; Veneziano, G.; Nugier, F.

    2011-01-01

    We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted ''geodesic light-cone'' coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called ''redshift drift'' in a generic inhomogeneous Universe

  9. Exact relativistic solution of disordered radiation with planar symmetry

    International Nuclear Information System (INIS)

    Teixeira, A.F. Da F.; Wolk, I.; Som, M.M.

    1977-01-01

    An exact solution of the Einstein equations corresponding to and equilibrium distribution of disordered electromagnetic radiation with planar symmetry is obtained. This equilibrium is due solely to the gravitational and pressure effects inherent to the radiation. The distribution of radiation is found to be maximum and finite at the plane of symmetry, and to decrease monotonically in directions normal to this plane. The solution tends asymptotically to the static plane symmetric vacuum solution obtained by Levi-Civita (Atti. Accad. Naz. Lincei Rc.; 27:240 (1918)). Time-like and null geodesics are discussed. (author)

  10. Divided Spheres Geodesics and the Orderly Subdivision of the Sphere

    CERN Document Server

    Popko, Edward S

    2012-01-01

    This well-illustrated book-in color throughout-presents a thorough introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.

  11. Geodesic Monitoring of Settling in Vertical Fuel Tanks

    Directory of Open Access Journals (Sweden)

    Luis Enrique Acosta-González

    2017-07-01

    Full Text Available The behavior of the settling in a vertical tank used for fuel storage was studied. Monitoring was conducted using the geodesic model for the geometric leveling of high accuracy category II. The original project varied during construction by replacing deep foundations with a surface one applying compaction techniques to improve soil resistance. The deformation values obtained provided valuable information on the implementation of the proposed foundation alternative depending on time and loads. The maximum settling was reported to be 132,6 mm. The displacements in the control points located in the perimeter of the tank had a distinct nature with a maximum of 44,2 mm, which caused the foundation structure to crack.

  12. Massive neutral particles on heterotic string theory

    International Nuclear Information System (INIS)

    Olivares, Marco; Villanueva, J.R.

    2013-01-01

    The motion of massive particles in the background of a charged black hole in heterotic string theory, which is characterized by a parameter α, is studied in detail in this paper. Since it is possible to write this space-time in the Einstein frame, we perform a quantitative analysis of the time-like geodesics by means of the standard Lagrange procedure. Thus, we obtain and solve a set of differential equations and then we describe the orbits in terms of the elliptic p-Weierstrass function. Also, by making an elementary derivation developed by Cornbleet (Am. J. Phys. 61(7):650-651, 1993) we obtain the correction to the angle of advance of perihelion to first order in α, and thus, by comparing with Mercury's data we give an estimation for the value of this parameter, which yields an heterotic solar charge Q s un ≅ 0.728 [Km]=0.493 M s un. Therefore, in addition to the study on null geodesics performed by Fernando (Phys. Rev. D 85:024033, 2012), this work completes the geodesic structure for this class of space-time. (orig.)

  13. Massive neutral particles on heterotic string theory

    Energy Technology Data Exchange (ETDEWEB)

    Olivares, Marco [Pontificia Universidad de Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Villanueva, J.R. [Universidad de Valparaiso, Departamento de Fisica y Astronomia, Valparaiso (Chile); Centro de Astrofisica de Valparaiso, Valparaiso (Chile)

    2013-12-15

    The motion of massive particles in the background of a charged black hole in heterotic string theory, which is characterized by a parameter {alpha}, is studied in detail in this paper. Since it is possible to write this space-time in the Einstein frame, we perform a quantitative analysis of the time-like geodesics by means of the standard Lagrange procedure. Thus, we obtain and solve a set of differential equations and then we describe the orbits in terms of the elliptic p-Weierstrass function. Also, by making an elementary derivation developed by Cornbleet (Am. J. Phys. 61(7):650-651, 1993) we obtain the correction to the angle of advance of perihelion to first order in {alpha}, and thus, by comparing with Mercury's data we give an estimation for the value of this parameter, which yields an heterotic solar charge Q{sub s}un {approx_equal} 0.728 [Km]=0.493 M{sub s}un. Therefore, in addition to the study on null geodesics performed by Fernando (Phys. Rev. D 85:024033, 2012), this work completes the geodesic structure for this class of space-time. (orig.)

  14. A hierarchical scheme for geodesic anatomical labeling of airway trees

    DEFF Research Database (Denmark)

    Feragen, Aasa; Petersen, Jens; Owen, Megan

    2012-01-01

    We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees....... In tree-space, the airway tree topology and geometry change continuously, giving a natural way to automatically handle anatomical differences and noise. The algorithm is made efficient using a hierarchical approach, in which labels are assigned from the top down. We only use features of the airway...

  15. Drift effects on electromagnetic geodesic acoustic modes

    Energy Technology Data Exchange (ETDEWEB)

    Sgalla, R. J. F., E-mail: reneesgalla@gmail.com [Institute of Physics, University of São Paulo, São Paulo 05508-900 (Brazil)

    2015-02-15

    A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in tokamak TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ{sub r} ∼ 25 cm, i.e., an order of magnitude higher than the usual value for zonal flows (ZFs)

  16. A geodesic atmospheric model with a quasi-Lagrangian vertical coordinate

    International Nuclear Information System (INIS)

    Heikes, Ross; Konor, Celal; Randall, David A

    2006-01-01

    The development of the Coupled Colorado State Model (CCoSM) is ultimately motivated by the need to predict and study climate change. All components of CCoSM innovatively blend unique design ideas and advanced computational techniques. The atmospheric model combines a geodesic horizontal grid with a quasi-Lagrangian vertical coordinate to improve the quality of simulations, particularly that of moisture and cloud distributions. Here we briefly describe the dynamical core, physical parameterizations and computational aspects of the atmospheric model, and present our preliminary numerical results. We also briefly discuss the rational behind our design choices and selection of computational techniques

  17. Maxwell fields and shear-free null geodesic congruences

    International Nuclear Information System (INIS)

    Newman, Ezra T

    2004-01-01

    We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principal null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors being proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the worldline. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, the following strange interpretation can be given. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x a take complex values, i.e., x a → z a = x a + iy a with complex metric g η ab dz a dz b , the real vacuum Maxwell equations can be extended into the complex space and rewritten as curl W=i W radical, div W=0 with W=E+iB. This subcase of Maxwell fields can then be extended into the complex space so as to have as source, a complex analytic worldline, i.e., to now become complex Lienard-Wiechart fields. When viewed as real fields on the real Minkowski space (z a = x a ), they possess a real principal null vector that is shear-free but twisting and diverging. The twist is a measure of how far the complex worldline is from the real 'slice'. Most Maxwell fields in this subcase are asymptotically flat with a time-varying set of electric and magnetic moments, all depending on the complex displacements and the complex velocities

  18. Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes

    Science.gov (United States)

    Stuchlík, Zdeněk; Schee, Jan

    2015-12-01

    In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.

  19. Geodesic acoustic modes excited by finite beta drift waves

    DEFF Research Database (Denmark)

    Chakrabarti, Nikhil Kumar; Guzdar, P.N.; Kleva, R.G.

    2008-01-01

    Presented in this paper is a mode-coupling analysis for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by finite beta drift waves. The finite beta effects give rise to a strong stabilizing influence on the parametric excitation process. The dominant finite beta...... effect is the combination of the Maxwell stress, which has a tendency to cancel the primary drive from the Reynolds stress, and the finite beta modification of the drift waves. The zonal magnetic field is also excited at the GAM frequency. However, it does not contribute to the overall stability...... of the three-wave process for parameters of relevance to the edge region of tokamaks....

  20. Nonlinear excitation of geodesic acoustic modes by drift waves

    International Nuclear Information System (INIS)

    Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.

    2007-01-01

    In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs

  1. Some investigations of null and time like geodesics in Schwarzschild and Schwarzschild de sitter black hole with a straight string passing through it

    International Nuclear Information System (INIS)

    Paudel, Eak Raj

    2007-01-01

    Gravitational field of Schwarzschild and Schwarzschild de-sitter Black hole with a straight string passing through it. In such space analytical and numerical solutions of null and time like geodesics are investigated. The string parameter a + is found to affect both the angle of deflection in null geodesics and the precession of perihelion on time like geodesics .It is seen that the deflection of null and time like geodesics near the gravitating mass of de-sitter space time increases with t he gravitational field of a straight string in flat space time has the property that the Newtonian potential vanishes yet there are non trivial gravitational effects. A test particle is neither attracted nor repelled by a string, yet the conical nature of space outside of string produces observable effects such as light deflection . Schwarzschild Black hole is a mathematical solution to the Einstein's field equations and corresponds to the gravitational field of massive compact spherically symmetric ob normal. References 1. Aryal, M.M, A. Vilenkin and L.H Ford, 1986, Phys.Rev. D32 ,2262 2. Moriyasu ,K ., 1980 , An introduction to gauge Invariance 3. Vilenkin A., 1985 , Physical reports , cosmic strings and Domain walls 4. Berry, M. , 1976 , Principle of cosmology and Gravitation 5. Mishner , C.W ., K.S .Throne , J.A wheeler , 1973. (Author)

  2. Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background

    International Nuclear Information System (INIS)

    Iftikhar, Sehrish; Sharif, M.

    2015-01-01

    This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole

  3. Three-dimensional black hole from a stringy anti endash de Sitter background

    International Nuclear Information System (INIS)

    Hjelmeland, S.E.

    1997-01-01

    A new black hole solution in 2+1 dimensions is found by taking cosmic strings as part of the vacuum structure of the anti endash de Sitter space-time. The solution has a structure that in many ways is similar to that of the Reissner-Nordstroem solution. With a vanishing cosmological constant, a space-time with a black hole of infinite extension appears with the inner horizon playing the role of a cosmological event horizon. The timelike and null geodesics are discussed. In particular it is shown that photons may follow conic sections. copyright 1997 The American Physical Society

  4. Gravitational lensing as a mechanism for effective cloaking

    International Nuclear Information System (INIS)

    Tippett, Benjamin K.

    2011-01-01

    In light of the surge in popularity of electromagnetic cloaking devices, we consider whether it is possible to use general relativity to cloak a volume of spacetime through gravitational lensing. We explore the cloaking properties of a spacetime through a ray-tracing procedure, wherein we plot the spatial trajectories of a congruence of initially parallel null geodesics as they cross the geometry. In this context, a cloaking device would cause all of the null geodesics in an initially parallel congruence incident upon the cloaking geometry to circumnavigate an internal region, and as the geodesics emerge from the geometry, they regain their original configuration. Thus, if gravitational lensing were used as a mechanism for cloaking, the internal region would be causally isolated from the external spacetime. For this reason, we propose an effective cloaking geometry wherein (only) most of ingoing null geodesics will splay away from a central region, and then regain their initial configuration as they exit the geometry. Thus, a compact object sitting within the effective cloaking geometry will impede a smaller cross section of the null congruence, and therefore appear optically smaller from all sides. We build our effective cloaking geometry by connecting a Minkowski spacetime exterior to a spherically symmetric, curved spacetime along a timelike hypersurface of constant radius using the Israel junction conditions. The junction conditions require a shell of matter of infinitesimal width confined to the junction surface. The matter required to build such a spacetime must violate the null energy condition.

  5. Structure of the effective potential for a spherical wormhole

    International Nuclear Information System (INIS)

    Montelongo Garcia, N.; Zannias, T.

    2008-01-01

    The structure of the effective potential V describing causal geodesics near the throat of an arbitrary spherical wormhole is analyzed. Einstein's equations relative to a set of regular coordinates covering a vicinity of the throat imply that any spherical wormhole can be constructed from solutions of an effective initial value problem with the throat serving as an initial value surface. The initial data involve matter variables, the area A(0) of the throat, and the gradient Λ(0) of the redshift factor on the throat. Whenever Λ(0)=0, the effective potential V has a critical point on the throat. Conditions upon the data are derived ensuring that the critical point is a local minimum (respectively maximum). For particular families of quasi-Schwarzschild wormholes, V exhibits a local minimum on the throat independently upon the energy E and angular momentum L 2 of the test particles and thus such wormholes admit stable circular timelike and null geodesics on the throat. For families of Chaplygin wormholes, we show that such geodesics are unstable. Based on a suitable power series representation of the metric, properties of V away from the throat are obtained that are useful for the analysis of accretion disks and radiation processes near the throat of any spherical wormhole.

  6. Electromagnetic characteristics of geodesic acoustic mode in the COMPASS tokamak

    Czech Academy of Sciences Publication Activity Database

    Seidl, Jakub; Krbec, Jaroslav; Hron, Martin; Adámek, Jiří; Hidalgo, C.; Markovič, Tomáš; Melnikov, A.V.; Stöckel, Jan; Weinzettl, Vladimír; Aftanas, Milan; Bílková, Petra; Bogár, Ondrej; Böhm, Petr; Eliseev, L.G.; Háček, Pavel; Havlíček, Josef; Horáček, Jan; Imríšek, Martin; Kovařík, Karel; Mitošinková, Klára; Pánek, Radomír; Tomeš, Matěj; Vondráček, Petr

    2017-01-01

    Roč. 57, č. 12 (2017), č. článku 126048. ISSN 0029-5515 R&D Projects: GA ČR(CZ) GA16-25074S; GA ČR(CZ) GA14-35260S; GA AV ČR(CZ) GA16-24724S; GA ČR(CZ) GA15-10723S; GA MŠk(CZ) 8D15001; GA MŠk(CZ) LM2015045 EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : geodesic acoustic mode * tokamak * turbulence * COMPASS Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 3.307, year: 2016

  7. Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava's gravity

    Science.gov (United States)

    Vieira, Ronaldo S. S.; Schee, Jan; Kluźniak, Włodek; Stuchlík, Zdeněk; Abramowicz, Marek

    2014-07-01

    We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Hořava's gravity. For any value of the Hořava parameter ω, there are values of the gravitational mass M for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of M, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.

  8. CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking

    Directory of Open Access Journals (Sweden)

    Evert van Aart

    2011-01-01

    Full Text Available Diffusion Tensor Imaging (DTI allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU. This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.

  9. Quasilocal contribution to the scalar self-force: Geodesic motion

    International Nuclear Information System (INIS)

    Ottewill, Adrian C.; Wardell, Barry

    2008-01-01

    We consider a scalar charge travelling in a curved background space-time. We calculate the quasilocal contribution to the scalar self-force experienced by such a particle following a geodesic in a general space-time. We also show that if we assume a massless field and a vacuum background space-time, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analogs are of immediate physical interest for the calculation of radiation-reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results

  10. Mean E×B shear effect on geodesic acoustic modes in Tokamaks

    International Nuclear Information System (INIS)

    Singh, Rameswar; Gurcan, Ozgur D.

    2015-01-01

    E × B shearing effect on geodesic acoustic mode (GAM) is investigated for the first time both as an initial value problem in the shearing frame and as an eigenvalue value problem in the lab frame. The nontrivial effects are that E × B shearing couples the standard GAM perturbations to their complimentary poloidal parities. The resulting GAM acquires an effective inertia increasing in time leading to GAM damping. Eigenmode analysis shows that GAMs are radially localized by E × B shearing with the mode width being inversely proportional and radial wave number directly proportional to the shearing rate for weak shear. (author)

  11. Measurement of the pion form factor in the time-like region for q2 values between 0.1 (GeV/c)2 and 0.18 (GeV/c)2

    International Nuclear Information System (INIS)

    Amendolia, S.R.; Badelek, B.; Bertolucci, E.; Bettoni, D.; Bizzeti, A.; Bosisio, L.; Bradaschia, C.; Dell'Orso, M.; Foa, L.; Focardi, E.; Giannetti, P.; Giazotto, A.; Giorgi, M.A.; Marrocchesi, P.S.; Menzione, A.; Ristori, L.; Scribano, A.; Tenchini, R.; Tonelli, G.; Triggiani, G.; Frank, S.G.F.; Harvey, J.; Menasce, D.; Meroni, E.; Moroni, L.; Milan Univ.

    1984-01-01

    The EM form factor of the pion has been studied in the time-like region by measuring sigma(e + e - ->π + π - ) normalization to sigma(e + e - ->μ + μ - ). Results have been obtained for q 2 down to the physical threshold. (orig.)

  12. (2+1)-dimensional pure gravity for an arbitrary closed initial surface

    International Nuclear Information System (INIS)

    Hosoya, Akio; Nakao, Ken-ichi.

    1989-04-01

    The (2+1)-dimensional pure Einstein gravity is studied in the ADM formalism. We completely solve the initial value and the time evolution problems with a closed Riemann surface being an initial surface, choosing the time slicing so that the trace of the extrinsic curvature is independent of spatial coordinates. The possible topology of the two-surface is either a torus or a Riemann surface of genus g≥2. It is shown that the moduli parameters of the torus follow the geodesic curve in the moduli space, while the motion of the moduli is static for the case g≥2. (author)

  13. YNOGK: A NEW PUBLIC CODE FOR CALCULATING NULL GEODESICS IN THE KERR SPACETIME

    Energy Technology Data Exchange (ETDEWEB)

    Yang Xiaolin; Wang Jiancheng, E-mail: yangxl@ynao.ac.cn [National Astronomical Observatories, Yunnan Observatory, Chinese Academy of Sciences, Kunming 650011 (China)

    2013-07-01

    Following the work of Dexter and Agol, we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass's and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter p, which is an integral value along the geodesic. This is the main difference between our code and previous similar ones. The advantage of this treatment is that the information about the turning points does not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles, and the observer-emitter problem, become root-finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as in Dexter and Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham and Bardeen have been extended, which allow one to readily handle situations in which the emitter or the observer has an arbitrary distance from, and motion state with respect to, the central compact object. The validation of the code has been extensively tested through applications to toy problems from the literature. The source FORTRAN code is freely available for download on our Web site http://www1.ynao.ac.cn/{approx}yangxl/yxl.html.

  14. YNOGK: A NEW PUBLIC CODE FOR CALCULATING NULL GEODESICS IN THE KERR SPACETIME

    International Nuclear Information System (INIS)

    Yang Xiaolin; Wang Jiancheng

    2013-01-01

    Following the work of Dexter and Agol, we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass's and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter p, which is an integral value along the geodesic. This is the main difference between our code and previous similar ones. The advantage of this treatment is that the information about the turning points does not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles, and the observer-emitter problem, become root-finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as in Dexter and Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham and Bardeen have been extended, which allow one to readily handle situations in which the emitter or the observer has an arbitrary distance from, and motion state with respect to, the central compact object. The validation of the code has been extensively tested through applications to toy problems from the literature. The source FORTRAN code is freely available for download on our Web site http://www1.ynao.ac.cn/~yangxl/yxl.html.

  15. a Fuzzy Automatic CAR Detection Method Based on High Resolution Satellite Imagery and Geodesic Morphology

    Science.gov (United States)

    Zarrinpanjeh, N.; Dadrassjavan, F.

    2017-09-01

    Automatic car detection and recognition from aerial and satellite images is mostly practiced for the purpose of easy and fast traffic monitoring in cities and rural areas where direct approaches are proved to be costly and inefficient. Towards the goal of automatic car detection and in parallel with many other published solutions, in this paper, morphological operators and specifically Geodesic dilation are studied and applied on GeoEye-1 images to extract car items in accordance with available vector maps. The results of Geodesic dilation are then segmented and labeled to generate primitive car items to be introduced to a fuzzy decision making system, to be verified. The verification is performed inspecting major and minor axes of each region and the orientations of the cars with respect to the road direction. The proposed method is implemented and tested using GeoEye-1 pansharpen imagery. Generating the results it is observed that the proposed method is successful according to overall accuracy of 83%. It is also concluded that the results are sensitive to the quality of available vector map and to overcome the shortcomings of this method, it is recommended to consider spectral information in the process of hypothesis verification.

  16. Racing a quantum computer through Minkowski spacetime

    International Nuclear Information System (INIS)

    Biamonte, Jacob D

    2010-01-01

    The Lorentzian length of a timelike curve connecting both endpoints of a computation in Minkowski spacetime is smaller than the Lorentzian length of the corresponding geodesic. In this talk, I will point out some properties of spacetime that allow an inertial classical computer to outperform a quantum one, at the completion of a long journey. We will focus on a comparison between the optimal quadratic Grover speed up from quantum computing and an n=2 speedup using classical computers and relativistic effects. These results are not practical as a new model of computation, but allow us to probe the ultimate limits physics places on computers.

  17. Cosmological model with anisotropic dark energy and self-similarity of the second kind

    International Nuclear Information System (INIS)

    Brandt, Carlos F. Charret; Silva, Maria de Fatima A. da; Rocha, Jaime F. Villas da; Chan, Roberto

    2006-01-01

    We study the evolution of an anisotropic fluid with self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (p r =ωρ) and that the fluid moves along time-like geodesics. The equation of state and the anisotropy with self-similarity of second kind imply ω = -1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that for the parameter α=-1/2 , it may represent a Big Rip cosmological model. (author)

  18. The power of general relativity

    International Nuclear Information System (INIS)

    Clifton, Timothy; Barrow, John D.

    2005-01-01

    We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to R 1+δ . This scale-free extension reduces to general relativity when δ→0. In order to constrain generalizations of general relativity of this power class, we analyze the behavior of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires δ>0 or δ -19 assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound 0≤δ -19 on theories of this type

  19. GEODESIC RECONSTRUCTION, SADDLE ZONES & HIERARCHICAL SEGMENTATION

    Directory of Open Access Journals (Sweden)

    Serge Beucher

    2011-05-01

    Full Text Available The morphological reconstruction based on geodesic operators, is a powerful tool in mathematical morphology. The general definition of this reconstruction supposes the use of a marker function f which is not necessarily related to the function g to be built. However, this paper deals with operations where the marker function is defined from given characteristic regions of the initial function f, as it is the case, for instance, for the extrema (maxima or minima but also for the saddle zones. Firstly, we show that the intuitive definition of a saddle zone is not easy to handle, especially when digitised images are involved. However, some of these saddle zones (regional ones also called overflow zones can be defined, this definition providing a simple algorithm to extract them. The second part of the paper is devoted to the use of these overflow zones as markers in image reconstruction. This reconstruction provides a new function which exhibits a new hierarchy of extrema. This hierarchy is equivalent to the hierarchy produced by the so-called waterfall algorithm. We explain why the waterfall algorithm can be achieved by performing a watershed transform of the function reconstructed by its initial watershed lines. Finally, some examples of use of this hierarchical segmentation are described.

  20. Equatorial Geodesics Around the Magnetars

    Science.gov (United States)

    Alfradique, Viviane A. P.; Troconis, Orlenys N.; Negreiros, Rodrigo P.

    Neutron stars manifest themselves as different classes of astrophysical sources that are associated to distinct phenomenology. Here we focus our attention on magnetars (or strongly magnetized neutron stars) that are associated to Soft Gamma Repeaters and Anomalous X-ray Pulsars. The magnetic field on surface of these objects, reaches values greater than 1015 G. Under intense magnetic fields, relativistic effects begin to be decisive for the definition of the structure and evolution of these objects. We are tempted to question ourselves to how strengths fields affect the structure of neutron star. In this work, our objective is study and compare two solutions of Einstein-Maxwell equations: the Bonnor solution, which is an analytical solution that describe the exterior spacetime for a massive compact object which has a magnetic field that is characterize as a dipole field and a complete solution that describe the interior and exterior spacetime for the same source found by numerical methods). For this, we describe the geodesic equations generated by such solutions. Our results show that the orbits generated by the Bonnor solution are the same as described by numerical solution. Also, show that the inclusion of magnetic fields with values up to 1017G in the center of the star does not modify sharply the particle orbits described around this star, so the use of Schwarzschild solution for the description of these orbits is a reasonable approximation.

  1. Causal inheritance in plane wave quotients

    International Nuclear Information System (INIS)

    Hubeny, Veronika E.; Rangamani, Mukund; Ross, Simon F.

    2003-01-01

    We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general spacetime to preserve stable causality. We explicitly show that the plane waves are stably causal; in passing, we observe that some pp-waves are not even distinguishing. We then consider the classification of all quotients of the maximally supersymmetric ten-dimensional plane wave under a spacelike isometry, and show that the quotient will lead to closed timelike curves iff the isometry involves a translation along the u direction. The appearance of these closed timelike curves is thus connected to the special properties of the light cones in plane wave spacetimes. We show that all other quotients preserve stable causality

  2. Causal inheritance in plane wave quotients

    Science.gov (United States)

    Hubeny, Veronika E.; Rangamani, Mukund; Ross, Simon F.

    2004-01-01

    We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general space-time to preserve stable causality. We explicitly show that the plane waves are stably causal; in passing, we observe that some pp waves are not even distinguishing. We then consider the classification of all quotients of the maximally supersymmetric ten-dimensional plane wave under a spacelike isometry, and show that the quotient will lead to closed timelike curves iff the isometry involves a translation along the u direction. The appearance of these closed timelike curves is thus connected to the special properties of the light cones in plane wave space-times. We show that all other quotients preserve stable causality.

  3. Rational first integrals of geodesic equations and generalised hidden symmetries

    International Nuclear Information System (INIS)

    Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

    2016-01-01

    We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson–O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski–Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing–Yano tensors. (paper)

  4. Properties of three-body decay functions derived with time-like jet calculus beyond leading order

    International Nuclear Information System (INIS)

    Sugiura, Tetsuya

    2002-01-01

    Three-body decay functions in time-like parton branching are calculated using the jet calculus to the next-to-leading logarithmic (NLL) order in perturbative quantum chromodynamics (QCD). The phase space contributions from each of the ladder diagrams and interference diagrams are presented. We correct part of the results for the three-body decay functions calculated previously by two groups. Employing our new results, the properties of the three-body decay functions in the regions of soft partons are examined numerically. Furthermore, we examine the contribution of the three-body decay functions modified by the restriction resulting from the kinematical boundary of the phase space for two-body decay in the parton shower model. This restriction leads to some problems for the parton shower model. For this reason, we propose a new restriction introduced by the kinematical boundary of the phase space for two-body decay. (author)

  5. On the (1 + 3) threading of spacetime with respect to an arbitrary timelike vector field

    Energy Technology Data Exchange (ETDEWEB)

    Bejancu, Aurel [Kuwait University, Department of Mathematics, P.O.Box 5969, Safat (Kuwait); Calin, Constantin [Technical University ' ' Gh.Asachi' ' , Department of Mathematics, Iasi (Romania)

    2015-04-15

    We develop a newapproach on the (1 + 3) threading of spacetime (M, g) with respect to a congruence of curves defined by an arbitrary timelike vector field. The study is based on spatial tensor fields and on theRiemannian spatial connection ∇*, which behave as 3D geometric objects. We obtain new formulas for local components of the Ricci tensor field of (M, g) with respect to the threading frame field, in terms of the Ricci tensor field of ∇* and of kinematic quantities. Also, new expressions for time covariant derivatives of kinematic quantities are stated. In particular, a new form of Raychaudhuri's equation enables us to prove Lemma 6.3, which completes a well-known lemma used in the proof of the Penrose-Hawking singularity theorems. Finally, we apply the new (1 + 3) formalism to the study of the dynamics of a Kerr-Newman black hole. (orig.)

  6. Nonlocal analysis of the excitation of the geodesic acoustic mode by drift waves

    DEFF Research Database (Denmark)

    Guzdar, P.N.; Kleva, R.G.; Chakrabarti, N.

    2009-01-01

    The geodesic acoustic modes (GAMs) are typically observed in the edge region of toroidal plasmas. Drift waves have been identified as a possible cause of excitation of GAMs by a resonant three wave parametric process. A nonlocal theory of excitation of these modes in inhomogeneous plasmas typical...... of the edge region of tokamaks is presented in this paper. The continuum GAM modes with coupling to the drift waves can create discrete "global" unstable eigenmodes localized in the edge "pedestal" region of the plasma. Multiple resonantly driven unstable radial eigenmodes can coexist on the edge pedestal....

  7. Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations

    DEFF Research Database (Denmark)

    Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren

    2010-01-01

    , we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations...... and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...

  8. Extraction of Generalized Parton Distributions from combined Deeply Virtual Compton Scattering and Timelike Compton scattering fits

    Science.gov (United States)

    Boer, Marie

    2017-09-01

    Generalized Parton Distributions (GPDs) contain the correlation between the parton's longitudinal momentum and their transverse distribution. They are accessed through hard exclusive processes, such as Deeply Virtual Compton Scattering (DVCS). DVCS has already been measured in several experiments and several models allow for extracting GPDs from these measurements. Timelike Compton Scattering (TCS) is, at leading order, the time-reversal equivalent process to DVCS and accesses GPDs at the same kinematics. Comparing GPDs extracted from DVCS and TCS is a unique way for proving GPD universality. Combining fits from the two processes will also allow for better constraining the GPDs. We will present our method for extracting GPDs from DVCS and TCS pseudo-data. We will compare fit results from the two processes in similar conditions and present what can be expected in term of contraints on GPDs from combined fits.

  9. A FUZZY AUTOMATIC CAR DETECTION METHOD BASED ON HIGH RESOLUTION SATELLITE IMAGERY AND GEODESIC MORPHOLOGY

    Directory of Open Access Journals (Sweden)

    N. Zarrinpanjeh

    2017-09-01

    Full Text Available Automatic car detection and recognition from aerial and satellite images is mostly practiced for the purpose of easy and fast traffic monitoring in cities and rural areas where direct approaches are proved to be costly and inefficient. Towards the goal of automatic car detection and in parallel with many other published solutions, in this paper, morphological operators and specifically Geodesic dilation are studied and applied on GeoEye-1 images to extract car items in accordance with available vector maps. The results of Geodesic dilation are then segmented and labeled to generate primitive car items to be introduced to a fuzzy decision making system, to be verified. The verification is performed inspecting major and minor axes of each region and the orientations of the cars with respect to the road direction. The proposed method is implemented and tested using GeoEye-1 pansharpen imagery. Generating the results it is observed that the proposed method is successful according to overall accuracy of 83%. It is also concluded that the results are sensitive to the quality of available vector map and to overcome the shortcomings of this method, it is recommended to consider spectral information in the process of hypothesis verification.

  10. Analytic continuation of tgensor fields along geodesics by covariant Taylor series

    International Nuclear Information System (INIS)

    Tsirulev, A.N.

    1995-01-01

    It is shown that in a certain normal neighborhood of a submanifold-the analog of a normal neighborhood of a point-the covariant derivatives of all orders of an arbitrary tensor field and of the curvature and torsion along geodesics normal to the submanifold, taken at points of the submanifold, determine under conditions of analyticity the given tensor field by Taylor series with tensor coefficients. Explicit expressions are obtained that provide a recursive procedure for calculating the coefficients of the series in any order. Special cases of the expansion of the components of a pseudo-Riemannian metric with respect to a metric connection without torsion for a point and hypersurface are considered

  11. D-branes in a big bang/big crunch universe: Nappi-Witten gauged WZW model

    Energy Technology Data Exchange (ETDEWEB)

    Hikida, Yasuaki [School of Physics and BK-21 Physics Division, Seoul National University, Seoul 151-747 (Korea, Republic of); Nayak, Rashmi R. [Dipartimento di Fisica and INFN, Sezione di Roma 2, ' Tor Vergata' ' , Rome 00133 (Italy); Panigrahi, Kamal L. [Dipartimento di Fisica and INFN, Sezione di Roma 2, ' Tor Vergata' , Rome 00133 (Italy)

    2005-05-01

    We study D-branes in the Nappi-Witten model, which is a gauged WZW model based on (SL(2,R) x SU(2))/(U(1) x U(1)). The model describes a four dimensional space-time consisting of cosmological regions with big bang/big crunch singularities and static regions with closed time-like curves. The aim of this paper is to investigate by D-brane probes whether there are pathologies associated with the cosmological singularities and the closed time-like curves. We first classify D-branes in a group theoretical way, and then examine DBI actions for effective theories on the D-branes. In particular, we show that D-brane metric from the DBI action does not include singularities, and wave functions on the D-branes are well behaved even in the presence of closed time-like curves.

  12. Existence and stability of circular orbits in general static and spherically symmetric spacetimes

    Science.gov (United States)

    Jia, Junji; Liu, Jiawei; Liu, Xionghui; Mo, Zhongyou; Pang, Xiankai; Wang, Yaoguang; Yang, Nan

    2018-02-01

    The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a necessary and sufficient condition on the metric function for the existence of timelike COs in SSS spacetimes. After analyzing the asymptotic behavior of the metric, we then show that asymptotic flat SSS spacetime that corresponds to a negative Newtonian potential at large r will always allow the existence of CO. The stability of the CO in a general SSS spacetime is then studied using the Lyapunov exponent method. Two sufficient conditions on the (in)stability of the COs are obtained. For null geodesics, a sufficient condition on the metric function for the (in)stability of null CO is also obtained. We then illustrate one powerful application of these results by showing that three SSS spacetimes whose metric function is not completely known will allow the existence of timelike and/or null COs. We also used our results to assert the existence and (in)stabilities of a number of known SSS metrics.

  13. Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches.

    Science.gov (United States)

    Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe

    2014-02-01

    In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.

  14. Postoperative radiotherapy for glioma: improved delineation of the clinical target volume using the geodesic distance calculation.

    Directory of Open Access Journals (Sweden)

    DanFang Yan

    Full Text Available OBJECTS: To introduce a new method for generating the clinical target volume (CTV from gross tumor volume (GTV using the geodesic distance calculation for glioma. METHODS: One glioblastoma patient was enrolled. The GTV and natural barriers were contoured on each slice of the computer tomography (CT simulation images. Then, a graphic processing unit based on a parallel Euclidean distance transform was used to generate the CTV considering natural barriers. Three-dimensional (3D visualization technique was applied to show the delineation results. Speed of operation and precision were compared between this new delineation method and the traditional method. RESULTS: In considering spatial barriers, the shortest distance from the point sheltered from these barriers equals the sum of the distance along the shortest path between the two points; this consists of several segments and evades the spatial barriers, rather than being the direct Euclidean distance between two points. The CTV was generated irregularly rather than as a spherical shape. The time required to generate the CTV was greatly reduced. Moreover, this new method improved inter- and intra-observer variability in defining the CTV. CONCLUSIONS: Compared with the traditional CTV delineation, this new method using geodesic distance calculation not only greatly shortens the time to modify the CTV, but also has better reproducibility.

  15. Stringy Jacobi fields in Morse theory

    International Nuclear Information System (INIS)

    Cho, Yong Seung; Hong, Soon-Tae

    2007-01-01

    We consider the variation of the surface spanned by closed strings in a spacetime manifold. Using the Nambu-Goto string action, we induce the geodesic surface equation and the geodesic surface deviation equation which yields a Jacobi field, and we define the index form of a geodesic surface as in the case of point particles to discuss conjugate strings on the geodesic surface

  16. Vacuum solutions admitting a geodesic null congruence with shear proportional to expansion

    International Nuclear Information System (INIS)

    Kupeli, A.H.

    1988-01-01

    Algebraically general, nontwisting solutions for the vacuum to vacuum generalized Kerr--Schild (GKS) transformation are obtained. These solutions admit a geodesic null congruence with shear proportional to expansion. In the Newman--Penrose formalism, if l/sup μ/ is chosen to be the null vector of the GKS transformation, this property is stated as σ = arho and Da = 0. It is assumed that a is a constant, and the background is chosen as a pp-wave solution. For generic values of a, the GKS metrics consist of the Kasner solutions. For a = +- (1 +- (2)/sup 1/2/), there are solutions with less symmetries including special cases of the Kota--Perjes and Lukacs solutions

  17. Twisting null geodesic congruences and the Einstein-Maxwell equations

    International Nuclear Information System (INIS)

    Newman, Ezra T; Silva-Ortigoza, Gilberto

    2006-01-01

    In a recent article, we returned to the study of asymptotically flat solutions of the vacuum Einstein equations with a rather unconventional point of view. The essential observation in that work was that from a given asymptotically flat vacuum spacetime with a given Bondi shear, one can find a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences where the class was uniquely given up to the arbitrary choice of a complex analytic 'worldline' in a four-dimensional complex space. By imitating certain terms in the Weyl tensor that are found in the algebraically special type II metrics, this complex worldline could be made unique and given-or assigned-the physical meaning as the complex centre of mass. Equations of motion for this case were found. The purpose of the present work is to extend those results to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically shear-free null geodesic congruences depending on a complex worldline in the same four-dimensional complex space. However in this case there will be, in general, two distinct but uniquely chosen worldlines, one of which can be assigned as the complex centre of charge while the other could be called the complex centre of mass. Rather than investigating the situation where there are two distinct complex worldlines, we study instead the special degenerate case where the two worldlines coincide, i.e., where there is a single unique worldline. This mimics the case of algebraically special Einstein-Maxwell fields where the degenerate principle null vector of the Weyl tensor coincides with a Maxwell principle null vector. Again we obtain equations of motion for this worldline-but explicitly found here only in an approximation. Though there are ambiguities in assigning physical meaning to different terms it appears as if reliance on the Kerr and charged Kerr metrics and classical electromagnetic radiation theory helps

  18. Study of the pion electromagnetic form factor in the timelike region, from the production threshold to 900 MeV in the center of mass

    International Nuclear Information System (INIS)

    Quenzer, A.

    1977-01-01

    The pion form factor is measured in the reaction e + e - →π + π - for center of mass energies in the range 480-900 MeV. The results are first analysed in terms of the conventional Vector Meson Dominance formalism, and then taking into account the ωπ inelastic channel. The results of this later formalisms is a pion form factor (F) which fits quite well all the existing data on F both in the timelike and spacelike regions, and a pion mean square radius [fr

  19. Quantum maps of geodesic flows on surfaces of constant negative curvature

    International Nuclear Information System (INIS)

    Bogomolny, E.B.; Carioli, M.

    1992-01-01

    The Selberg zeta function Z(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds Z(s) can be exactly rewritten as the Fredholm determinant det(1-T s ), where T s is the generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is presented, yielding a method to find not only the spectrum but also the eigenvalues of the Laplace-Beltrami operator in terms of eigenfunctions of T s . Various properties of the transfer operator are investigated both analytically and numerically. (author) 15 refs., 10 figs

  20. Geodesic mode instability driven by electron and ion fluxes during neutral beam injection in tokamaks

    Czech Academy of Sciences Publication Activity Database

    Camilo de Souza, F.; Elfimov, A.; Galvão, R.M.O.; Krbec, Jaroslav; Seidl, Jakub; Stöckel, Jan; Hron, Martin; Havlíček, Josef; Mitošinková, Klára

    2017-01-01

    Roč. 381, č. 36 (2017), s. 3066-3070 ISSN 0375-9601 R&D Projects: GA ČR(CZ) GA16-25074S; GA ČR(CZ) GA14-35260S; GA MŠk(CZ) 8D15001; GA MŠk(CZ) LM2015045 Institutional support: RVO:61389021 Keywords : Tokamak * Geodesic acoustic modes * Kinetic theory * Instability * Landau damping Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: 1.3 Physical sciences Impact factor: 1.772, year: 2016 http://www.sciencedirect.com/science/article/pii/S0375960117306989

  1. Collisions of massive particles, timelike thin shells and formation of black holes in three dimensions

    International Nuclear Information System (INIS)

    Lindgren, Jonathan

    2016-01-01

    We study collisions of massive pointlike particles in three dimensional anti-de Sitter space, generalizing the work on massless particles in http://dx.doi.org/10.1088/0264-9381/33/14/145009. We show how to construct exact solutions corresponding to the formation of either a black hole or a conical singularity from the collision of an arbitrary number of massive particles that fall in radially and collide at the origin of AdS. No restrictions on the masses or the angular and radial positions from where the particles are released, are imposed. We also consider the limit of an infinite number of particles, obtaining novel timelike thin shell spacetimes. These thin shells have an arbitrary mass distribution as well as a non-trivial embedding where the radial location of the shell depends on the angular coordinate, and we analyze these shells using the junction formalism of general relativity. We also consider the massless limit and find consistency with earlier results, as well as comment on the stress-energy tensor modes of the dual CFT.

  2. Collisions of massive particles, timelike thin shells and formation of black holes in three dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Lindgren, Jonathan [Theoretische Natuurkunde, Vrije Universiteit Brussel, and the International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Physique Théorique et Mathématique, Université Libre de Bruxelles,Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium)

    2016-12-13

    We study collisions of massive pointlike particles in three dimensional anti-de Sitter space, generalizing the work on massless particles in http://dx.doi.org/10.1088/0264-9381/33/14/145009. We show how to construct exact solutions corresponding to the formation of either a black hole or a conical singularity from the collision of an arbitrary number of massive particles that fall in radially and collide at the origin of AdS. No restrictions on the masses or the angular and radial positions from where the particles are released, are imposed. We also consider the limit of an infinite number of particles, obtaining novel timelike thin shell spacetimes. These thin shells have an arbitrary mass distribution as well as a non-trivial embedding where the radial location of the shell depends on the angular coordinate, and we analyze these shells using the junction formalism of general relativity. We also consider the massless limit and find consistency with earlier results, as well as comment on the stress-energy tensor modes of the dual CFT.

  3. Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

    Energy Technology Data Exchange (ETDEWEB)

    Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels (Belgium); Shabbir, A. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Hornung, G. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium)

    2016-11-15

    Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.

  4. Circuital model for the spherical geodesic waveguide perfect drain

    Science.gov (United States)

    González, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C.

    2012-08-01

    The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000.

  5. Circuital model for the spherical geodesic waveguide perfect drain

    International Nuclear Information System (INIS)

    González, Juan C; Grabovičkić, Dejan; Benítez, Pablo; Miñano, Juan C

    2012-01-01

    The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity that depends on frequency. However, this material is only a theoretical material, so it cannot be used in practical devices. The perfect drain has been claimed as necessary for achieving super-resolution (Leonhardt 2009 New J. Phys. 11 093040), which has increased the interest in practical perfect drains suitable for manufacturing. Here, we present a practical perfect drain that is designed using a simple circuit (made of a resistance and a capacitor) connected to the coaxial line. Moreover, we analyze the super-resolution properties of a device equivalent to the MFE, known as a spherical geodesic waveguide, loaded with this perfect drain. The super-resolution analysis for this device is carried out using COMSOL Multiphysics. The results of simulations predict a super-resolution of up to λ/3000. (paper)

  6. Light-cone observables and gauge-invariance in the geodesic light-cone formalism

    Energy Technology Data Exchange (ETDEWEB)

    Scaccabarozzi, Fulvio; Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zürich, Winterthurerstrasse 190, CH-8057, Zürich (Switzerland)

    2017-06-01

    The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.

  7. Optimal time travel in the Gödel universe

    Science.gov (United States)

    Natário, José

    2012-04-01

    Using the theory of optimal rocket trajectories in general relativity, recently developed in Henriques and Natário (2011), we present a candidate for the minimum total integrated acceleration closed timelike curve in the Gödel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament's conjectured value (Malament 1984), as was already implicit in the work of Manchak (Gen. Relativ. Gravit. 51-60, 2011); however, Malament's conjecture does seem to hold for periodic closed timelike curves.

  8. Straight spinning cosmic strings in Brans-Dicke gravity

    Science.gov (United States)

    Dos Santos, S. Mittmann; da Silva, J. M. Hoff; Cindra, J. L.

    2018-03-01

    An exact solution of straight spinning cosmic strings in Brans-Dicke theory of gravitation is presented. The possibility of the existence of closed time-like curves around these cosmic strings is analyzed. Furthermore, the stability about the formation of the topological defect discussed here is checked. It is shown that the existence of a suitable choice for the integration constants in which closed time-like curves are not allowed. We also study the (im)possibility of using the obtained spacetime in the rotational curves problem.

  9. Closed string field theory: Quantum action and the Batalin-Vilkovsky master equation

    International Nuclear Information System (INIS)

    Zwiebach, B.

    1993-01-01

    The complete quantum theory of covariant closed strings is constructed in detail. The nonpolynomial action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra L ∞ encoding the gauge symmetry of the classical theory. The higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation and thus consistent BRST quantization of the quantum action. From the L ∞ algebra, and the BV equation on the off-shell state space we derive the L ∞ algebra, and the BV equation on physical states that were recently constructed in d=2 string theory. The string diagrams are surfaces with minimal area metrics, foliated by closed geodesics of length 2π. These metrics generalize quadratic differentials in that foliation bands can cross. The string vertices are succinctly characterized; they include the surfaces whose foliation bands are all of height smaller than 2π. (orig.)

  10. Null Geodesics and Strong Field Gravitational Lensing of Black Hole with Global Monopole

    International Nuclear Information System (INIS)

    Iftikhar, Sehrish; Sharif, M.

    2015-01-01

    We study two interesting features of a black hole with an ordinary as well as phantom global monopole. Firstly, we investigate null geodesics which imply unstable orbital motion of particles for both cases. Secondly, we evaluate deflection angle in strong field regime. We then find Einstein rings, magnifications, and observables of the relativistic images for supermassive black hole at the center of galaxy NGC4486B. We also examine time delays for different galaxies and present our results numerically. It is found that the deflection angle for ordinary/phantom global monopole is greater/smaller than that of Schwarzschild black hole. In strong field limit, the remaining properties of these black holes are quite different from the Schwarzschild black hole

  11. A positive semi-definite action in a Kaluza-Klein theory with compactification onto time-like extra dimensions

    International Nuclear Information System (INIS)

    Pollock, M.D.

    1986-01-01

    We consider the (4+N)-dimensional theory whose Lagrangian function is Lsub(4+N)=√-g-circumflex α R-circumflex 2 , where R-circumflex is the Ricci scalar and α is a positive constant. The metric is g-circumflexsub(AB)= diag(gsub(ab), phi -1 g-barsub(mn)). Dimensional reduction leads to an effective four-dimensional Lagrangian of induced-gravity type. The positive semi-definiteness of L avoids the difficulties, pointed out recently by Horowitz and by Rubakov, which can arise in quantum cosmology when the (Euclidean) action becomes negative. The compactification is onto a time-like internal space g-barsub(mn), as suggested by Aref'eva and Volovich, giving a four-dimensional de Sitter space-time with phi=constant, which however is classically unstable on a time scale approx. H -1 . Decrease of the radius phisup(-1/2) of the internal space is ultimately halted by quantum effects, via some V(phi), and L 4 then includes the usual Hilbert term and a cosmological constant. (author)

  12. Approximate spacetime symmetries and conservation laws

    Energy Technology Data Exchange (ETDEWEB)

    Harte, Abraham I [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)], E-mail: harte@uchicago.edu

    2008-10-21

    A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.

  13. Extreme super-resolution using the spherical geodesic waveguide

    Science.gov (United States)

    Miñano, Juan Carlos; González, Juan Carlos; Benítez, Pablo; Grabovičkić, Dejan

    2012-06-01

    Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 super-resolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ /500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.

  14. Reversed sense of the ''outward'' direction for dynamical effects of rotation close to a Schwarzschild black hole

    International Nuclear Information System (INIS)

    Abramowicz, M.A.; Prasanna, A.R.

    1988-10-01

    Anderson and Lemos (1988) noticed that the direction in which viscous torque transports angular momentum changes, close to a black hole, from outwards to inwards. We find here that close to a black hole the centrifugal force attracts particles towards the hole. We argue that these are particular examples of a general reversal in sense of the inward and outward directions for all dynamical effects of rotation close to the hole. Using results from the recent paper by Abramowicz, Carter and Lasota (1988) we explain that the reversal is not connected with dragging of inertial frames or with the difference between the angular velocities of the hole and of the surrounding matter but rather, it is an effect of curvature. For a Schwarzschild black hole the reversal takes place at the circular photon orbit (r=3M-tilde) because the geodesic curvature, R-tilde=r(1-3M-tilde/r), of the circles r = const. changes its sign there. (author). 13 refs, 7 figs, 1 tab

  15. Timelike and null focusing singularities in spherical symmetry: A solution to the cosmological horizon problem and a challenge to the cosmic censorship hypothesis

    International Nuclear Information System (INIS)

    Celerier, Marie-Noeelle; Szekeres, Peter

    2002-01-01

    Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated by Szekeres and Iyer, we identify two classes of peculiar interest: focusing timelike singularity solutions with the stress-energy tensor of a radiative perfect fluid (equation of state: p=(1/3)ρ) and a set of null singularity classes verifying identical properties. We consider two important applications of these results: to cosmology, as regards the possibility of solving the horizon problem with no need to resort to any inflationary scenario, and to the strong cosmic censorship hypothesis to which we propose a class of physically consistent counterexamples

  16. Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

    Energy Technology Data Exchange (ETDEWEB)

    Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan, E-mail: zdenek.stuchlik@fpf.slu.cz, E-mail: jan.schee@fpf.slu.cz, E-mail: bobir.toshmatov@fpf.slu.cz, E-mail: jan.hladik@fpf.slu.cz, E-mail: jan.novotny@fpf.slu.cz [Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo náměstí 13, CZ-74601 Opava (Czech Republic)

    2017-06-01

    We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure p {sub c} to the central energy density ρ{sub c}, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N element of (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number ℓ > 50, while for smaller values of ℓ the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N ≥ 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10{sup −3} of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.

  17. GEODESIC MONITORING OF VERTICAL MOVEMENT OF JSC «GRODNO AZOT» BUILDINGS USING DIGITAL DNA 03 LEVEL

    Directory of Open Access Journals (Sweden)

    V. I. Mikhailov

    2010-01-01

    Full Text Available The paper presents peculiar features and methodology pertaining to application of digital DNA 03 level for monitoring vertical movement of load-carrying structures in the workshops and foundations of various capacities, exhaust pipes and granulation towers having height from 100 to150 meters. The proposed methods presuppose usage of the results of engineering and geological investigations and highly accurate geodesic measurements considered in the process of hydro- and pneumatic tests of an isothermic storage of liquid ammonia and a production “Ammonia” shop taken as an example. 

  18. Wormholes and timetravel

    International Nuclear Information System (INIS)

    Aichelburg, P.C.; Schein, F.

    1998-01-01

    We discuss a construction of a wormhole with the following properties: the wormhole connects to the same asymptotic region and is one-way traversable i.e. there exist timelike curves that start and end in the same asymptotic region and go through the wormhole. Moreover it is possible to satisfy the energy conditions. From any point in the asymptotic region there exist closed timelike curves. (author)

  19. From geodesics of the multipole solutions to the perturbed Kepler problem

    International Nuclear Information System (INIS)

    Hernandez-Pastora, J. L.; Ospino, J.

    2010-01-01

    A static and axisymmetric solution of the Einstein vacuum equations with a finite number of relativistic multipole moments (RMM) is written in multipole symmetry adapted (MSA) coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics, we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2 4 -pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.

  20. Near-Horizon Geodesics for Astrophysical and Idealised Black Holes: Coordinate Velocity and Coordinate Acceleration

    Directory of Open Access Journals (Sweden)

    Petarpa Boonserm

    2018-05-01

    Full Text Available Geodesics (by definition have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d 2 x i / d t 2 can very easily be non-zero, and the coordinate velocity d x i / d t can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit—for both astrophysical and idealised black holes—where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration d 2 x i / d t 2 is best interpreted in terms of horizon-penetrating coordinates.

  1. Precision Measurements of the Proton Electromagnetic Form Factors in the Time-Like Region and Vector Meson Spectroscopy

    CERN Multimedia

    2002-01-01

    The aim of this experiment is to measure with precision the electromagnetic form factors of the proton in the time-like region via the reaction: .ce @*p @A e|+e|- with antiprotons of momenta between 0 and 2 GeV/c. Up to @= 800 MeV/c, a continuous energy scan in @= 2 MeV (@]s) bins will be performed. The form factor !G(E)! and !G(M)! will be determined separately since large statistics can be collected with LEAR antiproton beams, so that angular distributions can be obtained at many momenta.\\\\ \\\\ In addition, e|+e|- pairs produced via the reaction: .ce @*p @A V|0 + neutrals, .ce !@A e|+e|- where the antiprotons are at rest, will be detected allowing the vector meson mass spectrum between @= 1 GeV and @= 1.7 GeV to be obtained with high statistics and in one run. \\\\ \\\\ The proposed apparatus consists of a central detector, surrounded by a gas Cerenkov counter, wire chambers, hodoscopes, and an electromagnetic calorimeter. The central detector consists of several layers of proportional chambers around a liquid-h...

  2. Fluid observers and tilting cosmology

    International Nuclear Information System (INIS)

    Coley, A A; Hervik, S; Lim, W C

    2006-01-01

    We study perfect fluid cosmological models with a constant equation of state parameter γ in which there are two naturally defined timelike congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence. We establish an appropriate set of boost formulae relating the physical variables, and consequently the observed quantities, in the two frames. We study expanding spatially homogeneous tilted perfect fluid models, with an emphasis on future evolution with extreme tilt. We show that for ultra-radiative equations of state (i.e. γ > 4/3), generically the tilt becomes extreme at late times and the fluid observers will reach infinite expansion within a finite proper time and experience a singularity similar to that of the big rip. In addition, we show that for sub-radiative equations of state (i.e. γ < 4/3), the tilt can become extreme at late times and give rise to an effective quintessential equation of state. To establish the connection with phantom cosmology and quintessence, we calculate the effective equation of state in the models under consideration and we determine the future asymptotic behaviour of the tilting models in the fluid frame variables using the boost formulae. We also discuss spatially inhomogeneous models and tilting spatially homogeneous models with a cosmological constant

  3. Black hole with quantum potential

    Energy Technology Data Exchange (ETDEWEB)

    Ali, Ahmed Farag, E-mail: ahmed.ali@fsc.bu.edu.eg [Department of Physics, Faculty of Science, Benha University, Benha 13518 (Egypt); Khalil, Mohammed M., E-mail: moh.m.khalil@gmail.com [Department of Electrical Engineering, Alexandria University, Alexandria 12544 (Egypt)

    2016-08-15

    In this work, we investigate black hole (BH) physics in the context of quantum corrections. These quantum corrections were introduced recently by replacing classical geodesics with quantal (Bohmian) trajectories and hence form a quantum Raychaudhuri equation (QRE). From the QRE, we derive a modified Schwarzschild metric, and use that metric to investigate BH singularity and thermodynamics. We find that these quantum corrections change the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. They prevent the BH from total evaporation, predicting the existence of a quantum BH remnant, which may introduce a possible resolution for the catastrophic behavior of Hawking radiation as the BH mass approaches zero. Those corrections also turn the spacelike singularity of the black hole to be timelike, and hence this may ameliorate the information loss problem.

  4. The Raychaudhuri equation in homogeneous cosmologies

    International Nuclear Information System (INIS)

    Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A.

    2014-01-01

    In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories

  5. Geodesic acoustic mode driven by energetic particles with bump-on-tail distribution

    Science.gov (United States)

    Ren, Haijun; Wang, Hao

    2018-04-01

    Energetic-particle-driven geodesic acoustic mode (EGAM) is analytically investigated by adopting the bump-on-tail distribution for energetic particles (EPs), which is created by the fact that the charge exchange time (τcx ) is sufficiently shorter than the slowing down time (τsl ). The dispersion relation is derived in the use of gyro-kinetic equations. Due to the finite ratio of the critical energy and the initial energy of EPs, defined as τc , the dispersion relation is numerically evaluated and the effect of finite τc is examined. Following relative simulation and experimental work, we specifically considered two cases: τsl/τcx = 3.4 and τsl/τcx = 20.4 . The pitch angle is shown to significantly enhance the growth rate and meanwhile, the real frequency is dramatically decreased with increasing pitch angle. The excitation of high-frequency EGAM is found, and this is consistent with both the experiment and the simulation. The number density effect of energetic particles, represented by \

  6. Tracking fuzzy borders using geodesic curves with application to liver segmentation on planning CT

    International Nuclear Information System (INIS)

    Yuan, Yading; Chao, Ming; Sheu, Ren-Dih; Rosenzweig, Kenneth; Lo, Yeh-Chi

    2015-01-01

    Purpose: This work aims to develop a robust and efficient method to track the fuzzy borders between liver and the abutted organs where automatic liver segmentation usually suffers, and to investigate its applications in automatic liver segmentation on noncontrast-enhanced planning computed tomography (CT) images. Methods: In order to track the fuzzy liver–chestwall and liver–heart borders where oversegmentation is often found, a starting point and an ending point were first identified on the coronal view images; the fuzzy border was then determined as a geodesic curve constructed by minimizing the gradient-weighted path length between these two points near the fuzzy border. The minimization of path length was numerically solved by fast-marching method. The resultant fuzzy borders were incorporated into the authors’ automatic segmentation scheme, in which the liver was initially estimated by a patient-specific adaptive thresholding and then refined by a geodesic active contour model. By using planning CT images of 15 liver patients treated with stereotactic body radiation therapy, the liver contours extracted by the proposed computerized scheme were compared with those manually delineated by a radiation oncologist. Results: The proposed automatic liver segmentation method yielded an average Dice similarity coefficient of 0.930 ± 0.015, whereas it was 0.912 ± 0.020 if the fuzzy border tracking was not used. The application of fuzzy border tracking was found to significantly improve the segmentation performance. The mean liver volume obtained by the proposed method was 1727 cm 3 , whereas it was 1719 cm 3 for manual-outlined volumes. The computer-generated liver volumes achieved excellent agreement with manual-outlined volumes with correlation coefficient of 0.98. Conclusions: The proposed method was shown to provide accurate segmentation for liver in the planning CT images where contrast agent is not applied. The authors’ results also clearly demonstrated

  7. Diviner lunar radiometer gridded brightness temperatures from geodesic binning of modeled fields of view

    Science.gov (United States)

    Sefton-Nash, E.; Williams, J.-P.; Greenhagen, B. T.; Aye, K.-M.; Paige, D. A.

    2017-12-01

    An approach is presented to efficiently produce high quality gridded data records from the large, global point-based dataset returned by the Diviner Lunar Radiometer Experiment aboard NASA's Lunar Reconnaissance Orbiter. The need to minimize data volume and processing time in production of science-ready map products is increasingly important with the growth in data volume of planetary datasets. Diviner makes on average >1400 observations per second of radiance that is reflected and emitted from the lunar surface, using 189 detectors divided into 9 spectral channels. Data management and processing bottlenecks are amplified by modeling every observation as a probability distribution function over the field of view, which can increase the required processing time by 2-3 orders of magnitude. Geometric corrections, such as projection of data points onto a digital elevation model, are numerically intensive and therefore it is desirable to perform them only once. Our approach reduces bottlenecks through parallel binning and efficient storage of a pre-processed database of observations. Database construction is via subdivision of a geodesic icosahedral grid, with a spatial resolution that can be tailored to suit the field of view of the observing instrument. Global geodesic grids with high spatial resolution are normally impractically memory intensive. We therefore demonstrate a minimum storage and highly parallel method to bin very large numbers of data points onto such a grid. A database of the pre-processed and binned points is then used for production of mapped data products that is significantly faster than if unprocessed points were used. We explore quality controls in the production of gridded data records by conditional interpolation, allowed only where data density is sufficient. The resultant effects on the spatial continuity and uncertainty in maps of lunar brightness temperatures is illustrated. We identify four binning regimes based on trades between the

  8. VizieR Online Data Catalog: Bessel (1825) calculation for geodesic measurements (Karney+, 2010)

    Science.gov (United States)

    Karney, C. F. F.; Deakin, R. E.

    2010-06-01

    The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table, -4.4, should be parsed as "-4" (the characteristic) and ".4" (the mantissa); the anti-log for this entry is 10(-4+0.4)=2.5e-4. The "Delta" columns give the first difference of the preceding column, i.e., the difference of the preceding column in the next row and the preceding column in the current row. In the printed tables these are expressed as "units in the last place" and the differences are of the rounded representations in the preceding columns (to minimize interpolation errors). In table1.dat these are given scaled to a match the format used for the preceding column, as indicated by the units given for these columns. The unit log(") (in the description within square brackets [arcsec]) means the logarithm of a quantity expressed in arcseconds. (3 data files).

  9. Geodesics of electrically and magnetically charged test particles in the Reissner-Nordstroem space-time: Analytical solutions

    International Nuclear Information System (INIS)

    Grunau, Saskia; Kagramanova, Valeria

    2011-01-01

    We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstroem space-time in terms of the Weierstrass weierp, σ, and ζ elliptic functions. Based on the study of the polynomials in the θ and r equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstroem space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstroem space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

  10. Black hole with quantum potential

    Directory of Open Access Journals (Sweden)

    Ahmed Farag Ali

    2016-08-01

    Full Text Available In this work, we investigate black hole (BH physics in the context of quantum corrections. These quantum corrections were introduced recently by replacing classical geodesics with quantal (Bohmian trajectories and hence form a quantum Raychaudhuri equation (QRE. From the QRE, we derive a modified Schwarzschild metric, and use that metric to investigate BH singularity and thermodynamics. We find that these quantum corrections change the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. They prevent the BH from total evaporation, predicting the existence of a quantum BH remnant, which may introduce a possible resolution for the catastrophic behavior of Hawking radiation as the BH mass approaches zero. Those corrections also turn the spacelike singularity of the black hole to be timelike, and hence this may ameliorate the information loss problem.

  11. Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries

    International Nuclear Information System (INIS)

    Field, Scott E; Hesthaven, Jan S; Lau, Stephen R

    2009-01-01

    Gravitational wave emission from extreme mass ratio binaries (EMRBs) should be detectable by the joint NASA-ESA LISA project, spurring interest in analytical and numerical methods for investigating EMRBs. We describe a discontinuous Galerkin (dG) method for solving the distributionally forced 1+1 wave equations which arise when modeling EMRBs via the perturbation theory of Schwarzschild black holes. Despite the presence of jump discontinuities in the relevant polar and axial gravitational 'master functions', our dG method achieves global spectral accuracy, provided that we know the instantaneous position, velocity and acceleration of the small particle. Here these variables are known, since we assume that the particle follows a timelike geodesic of the Schwarzschild geometry. We document the results of several numerical experiments testing our method, and in our concluding section discuss the possible inclusion of gravitational self-force effects.

  12. Geodesically complete BTZ-type solutions of 2  +  1 Born–Infeld gravity

    International Nuclear Information System (INIS)

    Bazeia, D; Losano, L; Olmo, Gonzalo J; Rubiera-Garcia, D

    2017-01-01

    We study Born–Infeld gravity coupled to a static, non-rotating electric field in 2  +  1 dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of general relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on their innermost region. This seems to be a generic prediction of extensions of general relativity formulated in metric-affine (or Palatini) spaces, where metric and connection are regarded as independent degrees of freedom. (paper)

  13. Beyond the geodesic approximation: Conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole

    International Nuclear Information System (INIS)

    Barack, Leor; Sago, Norichika

    2011-01-01

    We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass μ is much smaller than the black hole mass M, and explore post-geodesic corrections of O(μ/M). Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the O(μ/M) conservative correction to the periastron advance of the orbit, as a function of the (gauge-dependent) semilatus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit ''redshift'' invariant. We compute the O(μ/M) conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak-field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations.

  14. Dust of dark energy

    International Nuclear Information System (INIS)

    Lim, Eugene A.; Sawicki, Ignacy; Vikman, Alexander

    2010-01-01

    We introduce a novel class of field theories where energy always flows along timelike geodesics, mimicking in that respect dust, yet which possess non-zero pressure. This theory comprises two scalar fields, one of which is a Lagrange multiplier enforcing a constraint between the other's field value and derivative. We show that this system possesses no wave-like modes but retains a single dynamical degree of freedom. Thus, the sound speed is always identically zero on all backgrounds. In particular, cosmological perturbations reproduce the standard behaviour for hydrodynamics in the limit of vanishing sound speed. Using all these properties we propose a model unifying Dark Matter and Dark Energy in a single degree of freedom. In a certain limit this model exactly reproduces the evolution history of ΛCDM, while deviations away from the standard expansion history produce a potentially measurable difference in the evolution of structure

  15. Singularities and the geometry of spacetime

    Science.gov (United States)

    Hawking, Stephen

    2014-11-01

    The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove

  16. MHD-model for low-frequency waves in a tokamak with toroidal plasma rotation and problem of existence of global geodesic acoustic modes

    Energy Technology Data Exchange (ETDEWEB)

    Lakhin, V. P.; Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com, E-mail: vilkiae@gmail.com; Ilgisonis, V. I. [National Research Centre Kurchatov Institute (Russian Federation); Konovaltseva, L. V. [Peoples’ Friendship University of Russia (Russian Federation)

    2015-12-15

    A set of reduced linear equations for the description of low-frequency perturbations in toroidally rotating plasma in axisymmetric tokamak is derived in the framework of ideal magnetohydrodynamics. The model suitable for the study of global geodesic acoustic modes (GGAMs) is designed. An example of the use of the developed model for derivation of the integral conditions for GGAM existence and of the corresponding dispersion relation is presented. The paper is dedicated to the memory of academician V.D. Shafranov.

  17. SU-F-R-05: Multidimensional Imaging Radiomics-Geodesics: A Novel Manifold Learning Based Automatic Feature Extraction Method for Diagnostic Prediction in Multiparametric Imaging

    Energy Technology Data Exchange (ETDEWEB)

    Parekh, V [The Johns Hopkins University, Computer Science. Baltimore, MD (United States); Jacobs, MA [The Johns Hopkins University School of Medicine, Dept of Radiology and Oncology. Baltimore, MD (United States)

    2016-06-15

    Purpose: Multiparametric radiological imaging is used for diagnosis in patients. Potentially extracting useful features specific to a patient’s pathology would be crucial step towards personalized medicine and assessing treatment options. In order to automatically extract features directly from multiparametric radiological imaging datasets, we developed an advanced unsupervised machine learning algorithm called the multidimensional imaging radiomics-geodesics(MIRaGe). Methods: Seventy-six breast tumor patients underwent 3T MRI breast imaging were used for this study. We tested the MIRaGe algorithm to extract features for classification of breast tumors into benign or malignant. The MRI parameters used were T1-weighted, T2-weighted, dynamic contrast enhanced MR imaging (DCE-MRI) and diffusion weighted imaging(DWI). The MIRaGe algorithm extracted the radiomics-geodesics features (RGFs) from multiparametric MRI datasets. This enable our method to learn the intrinsic manifold representations corresponding to the patients. To determine the informative RGF, a modified Isomap algorithm(t-Isomap) was created for a radiomics-geodesics feature space(tRGFS) to avoid overfitting. Final classification was performed using SVM. The predictive power of the RGFs was tested and validated using k-fold cross validation. Results: The RGFs extracted by the MIRaGe algorithm successfully classified malignant lesions from benign lesions with a sensitivity of 93% and a specificity of 91%. The top 50 RGFs identified as the most predictive by the t-Isomap procedure were consistent with the radiological parameters known to be associated with breast cancer diagnosis and were categorized as kinetic curve characterizing RGFs, wash-in rate characterizing RGFs, wash-out rate characterizing RGFs and morphology characterizing RGFs. Conclusion: In this paper, we developed a novel feature extraction algorithm for multiparametric radiological imaging. The results demonstrated the power of the MIRa

  18. SU-F-R-05: Multidimensional Imaging Radiomics-Geodesics: A Novel Manifold Learning Based Automatic Feature Extraction Method for Diagnostic Prediction in Multiparametric Imaging

    International Nuclear Information System (INIS)

    Parekh, V; Jacobs, MA

    2016-01-01

    Purpose: Multiparametric radiological imaging is used for diagnosis in patients. Potentially extracting useful features specific to a patient’s pathology would be crucial step towards personalized medicine and assessing treatment options. In order to automatically extract features directly from multiparametric radiological imaging datasets, we developed an advanced unsupervised machine learning algorithm called the multidimensional imaging radiomics-geodesics(MIRaGe). Methods: Seventy-six breast tumor patients underwent 3T MRI breast imaging were used for this study. We tested the MIRaGe algorithm to extract features for classification of breast tumors into benign or malignant. The MRI parameters used were T1-weighted, T2-weighted, dynamic contrast enhanced MR imaging (DCE-MRI) and diffusion weighted imaging(DWI). The MIRaGe algorithm extracted the radiomics-geodesics features (RGFs) from multiparametric MRI datasets. This enable our method to learn the intrinsic manifold representations corresponding to the patients. To determine the informative RGF, a modified Isomap algorithm(t-Isomap) was created for a radiomics-geodesics feature space(tRGFS) to avoid overfitting. Final classification was performed using SVM. The predictive power of the RGFs was tested and validated using k-fold cross validation. Results: The RGFs extracted by the MIRaGe algorithm successfully classified malignant lesions from benign lesions with a sensitivity of 93% and a specificity of 91%. The top 50 RGFs identified as the most predictive by the t-Isomap procedure were consistent with the radiological parameters known to be associated with breast cancer diagnosis and were categorized as kinetic curve characterizing RGFs, wash-in rate characterizing RGFs, wash-out rate characterizing RGFs and morphology characterizing RGFs. Conclusion: In this paper, we developed a novel feature extraction algorithm for multiparametric radiological imaging. The results demonstrated the power of the MIRa

  19. Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity

    International Nuclear Information System (INIS)

    Amarilla, Leonardo; Eiroa, Ernesto F.; Giribet, Gaston

    2010-01-01

    The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first-class Pontryagin density. In this theory, which has attracted considerable attention recently, the Schwarzschild metric persists as an exact solution, and this is why this model resists several observational constraints. In contrast, the spinning black hole solution of the theory is not given by the Kerr metric but by a modification of it, so far only known for slow rotation and small coupling constant. In the present paper, we show that, in this approximation, the null geodesic equation can be integrated, and this allows us to investigate the shadow cast by a black hole. We discuss how, in addition to the angular momentum of the solution, the coupling to the Chern-Simons term deforms the shape of the shadow.

  20. Quantum mechanics of time travel through post-selected teleportation

    International Nuclear Information System (INIS)

    Lloyd, Seth; Garcia-Patron, Raul; Maccone, Lorenzo; Giovannetti, Vittorio; Shikano, Yutaka

    2011-01-01

    This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch's theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.

  1. Supersymmetric warped AdS in extended topologically massive supergravity

    International Nuclear Information System (INIS)

    Deger, N.S.; Kaya, A.; Samtleben, H.; Sezgin, E.

    2014-01-01

    We determine the most general form of off-shell N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell supergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS 3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS 3 . This occurs when the coefficient of the Lorentz–Chern–Simons term is related to the AdS radius by μℓ=2. We find that the spacelike-squashed AdS 3 can be modded out by a suitable discrete subgroup of the isometry group, yielding an extremal black hole solution which avoids closed timelike curves

  2. Giant wormholes in ghost-free bigravity theory

    Energy Technology Data Exchange (ETDEWEB)

    Sushkov, Sergey V.; Volkov, Mikhail S., E-mail: sergey_sushkov@mail.ru, E-mail: volkov@lmpt.univ-tours.fr [Department of General Relativity and Gravitation, Institute of Physics, Kazan Federal University, Kremlevskaya street 18, 420008 Kazan (Russian Federation)

    2015-06-01

    We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we call W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.

  3. Giant wormholes in ghost-free bigravity theory

    Energy Technology Data Exchange (ETDEWEB)

    Sushkov, Sergey V. [Department of General Relativity and Gravitation, Institute of Physics,Kazan Federal University, Kremlevskaya street 18, 420008 Kazan (Russian Federation); Volkov, Mikhail S. [Department of General Relativity and Gravitation, Institute of Physics,Kazan Federal University, Kremlevskaya street 18, 420008 Kazan (Russian Federation); Laboratoire de Mathématiques et Physique Théorique CNRS-UMR 7350, Université de Tours, Parc de Grandmont, 37200 Tours (France)

    2015-06-09

    We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we call W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.

  4. Rapid geodesic mapping of brain functional connectivity: implementation of a dedicated co-processor in a field-programmable gate array (FPGA) and application to resting state functional MRI.

    Science.gov (United States)

    Minati, Ludovico; Cercignani, Mara; Chan, Dennis

    2013-10-01

    Graph theory-based analyses of brain network topology can be used to model the spatiotemporal correlations in neural activity detected through fMRI, and such approaches have wide-ranging potential, from detection of alterations in preclinical Alzheimer's disease through to command identification in brain-machine interfaces. However, due to prohibitive computational costs, graph-based analyses to date have principally focused on measuring connection density rather than mapping the topological architecture in full by exhaustive shortest-path determination. This paper outlines a solution to this problem through parallel implementation of Dijkstra's algorithm in programmable logic. The processor design is optimized for large, sparse graphs and provided in full as synthesizable VHDL code. An acceleration factor between 15 and 18 is obtained on a representative resting-state fMRI dataset, and maps of Euclidean path length reveal the anticipated heterogeneous cortical involvement in long-range integrative processing. These results enable high-resolution geodesic connectivity mapping for resting-state fMRI in patient populations and real-time geodesic mapping to support identification of imagined actions for fMRI-based brain-machine interfaces. Copyright © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.

  5. Geodesic Flow Kernel Support Vector Machine for Hyperspectral Image Classification by Unsupervised Subspace Feature Transfer

    Directory of Open Access Journals (Sweden)

    Alim Samat

    2016-03-01

    Full Text Available In order to deal with scenarios where the training data, used to deduce a model, and the validation data have different statistical distributions, we study the problem of transformed subspace feature transfer for domain adaptation (DA in the context of hyperspectral image classification via a geodesic Gaussian flow kernel based support vector machine (GFKSVM. To show the superior performance of the proposed approach, conventional support vector machines (SVMs and state-of-the-art DA algorithms, including information-theoretical learning of discriminative cluster for domain adaptation (ITLDC, joint distribution adaptation (JDA, and joint transfer matching (JTM, are also considered. Additionally, unsupervised linear and nonlinear subspace feature transfer techniques including principal component analysis (PCA, randomized nonlinear principal component analysis (rPCA, factor analysis (FA and non-negative matrix factorization (NNMF are investigated and compared. Experiments on two real hyperspectral images show the cross-image classification performances of the GFKSVM, confirming its effectiveness and suitability when applied to hyperspectral images.

  6. Stationary metrics and optical Zermelo-Randers-Finsler geometry

    International Nuclear Information System (INIS)

    Gibbons, G. W.; Warnick, C. M.; Herdeiro, C. A. R.; Werner, M. C.

    2009-01-01

    We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalization of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various issues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo surface in the spacetime picture. The gauge equivalence in this network of relations is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.

  7. Black holes in the ghost condensate

    International Nuclear Information System (INIS)

    Mukohyama, Shinji

    2005-01-01

    We investigate how the ghost condensate reacts to black holes immersed in it. A ghost condensate defines a hypersurface-orthogonal congruence of timelike curves, each of which has the tangent vector u μ =-g μν ∂ ν φ. It is argued that the ghost condensate in this picture approximately corresponds to a congruence of geodesics. In other words, the ghost condensate accretes into a black hole just like a pressureless dust. Correspondingly, if the energy density of the ghost condensate at large distance is set to an extremely small value by cosmic expansion then the late-time accretion rate of the ghost condensate should be negligible. The accretion rate remains very small even if effects of higher derivative terms are taken into account, provided that the black hole is sufficiently large. It is also discussed how to reconcile the black-hole accretion with the possibility that the ghost condensate might behave like dark matter

  8. Geodesic paths and topological charges in quantum systems

    Science.gov (United States)

    Grangeiro Souza Barbosa Lima, Tiago Aecio

    This dissertation focuses on one question: how should one drive an experimentally prepared state of a generic quantum system into a different target-state, simultaneously minimizing energy dissipation and maximizing the fidelity between the target and evolved-states? We develop optimal adiabatic driving protocols for general quantum systems, and show that these are geodesic paths. Geometric ideas have always played a fundamental role in the understanding and unification of physical phenomena, and the recent discovery of topological insulators has drawn great interest to topology from the field of condensed matter physics. Here, we discuss the quantum geometric tensor, a mathematical object that encodes geometrical and topological properties of a quantum system. It is related to the fidelity susceptibility (an important quantity regarding quantum phase transitions) and to the Berry curvature, which enables topological characterization through Berry phases. A refined understanding of the interplay between geometry and topology in quantum mechanics is of direct relevance to several emergent technologies, such as quantum computers, quantum cryptography, and quantum sensors. As a demonstration of how powerful geometric and topological ideas can become when combined, we present the results of an experiment that we recently proposed. This experimental work was done at the Google Quantum Lab, where researchers were able to visualize the topological nature of a two-qubit system in sharp detail, a startling contrast with earlier methods. To achieve this feat, the optimal protocols described in this dissertation were used, allowing for a great improvement on the experimental apparatus, without the need for technical engineering advances. Expanding the existing literature on the quantum geometric tensor using notions from differential geometry and topology, we build on the subject nowadays known as quantum geometry. We discuss how slowly changing a parameter of a quantum

  9. Effects of plasma current on nonlinear interactions of ITG turbulence, zonal flows and geodesic acoustic modes

    International Nuclear Information System (INIS)

    Angelino, P; Bottino, A; Hatzky, R; Jolliet, S; Sauter, O; Tran, T M; Villard, L

    2006-01-01

    The mutual interactions of ion temperature gradient (ITG) driven modes, zonal flows and geodesic acoustic modes (GAM) in tokamak plasmas are investigated using a global nonlinear gyrokinetic formulation with totally unconstrained evolution of temperature gradient and profile. A series of numerical simulations with the same initial temperature and density profile specifications is performed using a sequence of ideal MHD equilibria differing only in the value of the total plasma current, in particular with identical magnetic shear profiles and shapes of magnetic surfaces. On top of a bursty or quasi-steady state behaviour the zonal flows oscillate at the GAM frequency. The amplitude of these oscillations increases with the value of the safety factor q, resulting in a less effective suppression of ITG turbulence by zonal flows at a lower plasma current. The turbulence-driven volume-averaged radial heat transport is found to scale inversely with the total plasma current

  10. Light cones in relativity: Real, complex, and virtual, with applications

    International Nuclear Information System (INIS)

    Adamo, T. M.; Newman, E. T.

    2011-01-01

    We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and asymptotically flat settings, complexified future null infinity I C + acts as a ''holographic screen,'' interpolating between two dual descriptions of the null geodesic congruence. One description constructs a complex null geodesic congruence in a complex space-time whose source is a complex worldline, a virtual source as viewed from the holographic screen. This complex null geodesic congruence intersects the real asymptotic boundary when its source lies on a particular open-string type structure in the complex space-time. The other description constructs a real, twisting, shear-free or asymptotically shear-free null geodesic congruence in the real space-time, whose source (at least in Minkowski space) is in general a closed-string structure: the caustic set of the congruence. Finally we show that virtually all of the interior space-time physical quantities that are identified at null infinity I + (center of mass, spin, angular momentum, linear momentum, and force) are given kinematic meaning and dynamical descriptions in terms of the complex worldline.

  11. Cubic and quartic integrals for geodesic flow on 2-torus via a system of the hydrodynamic type

    International Nuclear Information System (INIS)

    Bialy, Misha; Mironov, Andrey E

    2011-01-01

    In this paper, we deal with the classical question of the existence of polynomials in momenta integrals for geodesic flows on the 2-torus. For the quasilinear system on the coefficients of the polynomial integral, we investigate the region (so-called elliptic region) where two of the eigenvalues are complex conjugate. We show that for quartic integrals the other two eigenvalues are real and necessarily genuinely nonlinear. This observation, together with the property of the system to be rich (semi-Hamiltonian), enables us to classify elliptic regions completely. We prove that on these regions the integral is always reducible. The case of complex-conjugate eigenvalues for the system corresponding to the integral of degree 3 is done similarly. These results show that if new integrable examples exist, they can be found only within the region of hyperbolicity of the quasilinear system

  12. Negative branes, supergroups and the signature of spacetime

    Science.gov (United States)

    Dijkgraaf, Robbert; Heidenreich, Ben; Jefferson, Patrick; Vafa, Cumrun

    2018-02-01

    We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0| N) supergroup theories are holographically dual to an exotic variant of type IIB string theory on {dS}_{3,2}× {\\overline{S}}^5 , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for N=2 SU( N | M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

  13. An obstacle to building a time machine

    International Nuclear Information System (INIS)

    Carroll, S.M.; Farhi, E.; Guth, A.H.

    1992-01-01

    Gott has shown that a spacetime with two infinite parallel cosmic strings passing each other with sufficient velocity contains closed timelike curves. We discuss an attempt to build such a time machine. Using the energy-momentum conservation laws in the equivalent (2+1)-dimensional theory, we explicitly construct the spacetime representing the decay of one gravitating particle into two. We find that there is never enough mass in an open universe to build the time machine from the products of decays of stationary particles. More generally, the Gott time machine cannot exist in any open (2+1)-dimensional universe for which the total momentum is timelike

  14. Computerized liver volumetry on MRI by using 3D geodesic active contour segmentation.

    Science.gov (United States)

    Huynh, Hieu Trung; Karademir, Ibrahim; Oto, Aytekin; Suzuki, Kenji

    2014-01-01

    Our purpose was to develop an accurate automated 3D liver segmentation scheme for measuring liver volumes on MRI. Our scheme for MRI liver volumetry consisted of three main stages. First, the preprocessing stage was applied to T1-weighted MRI of the liver in the portal venous phase to reduce noise and produce the boundary-enhanced image. This boundary-enhanced image was used as a speed function for a 3D fast-marching algorithm to generate an initial surface that roughly approximated the shape of the liver. A 3D geodesic-active-contour segmentation algorithm refined the initial surface to precisely determine the liver boundaries. The liver volumes determined by our scheme were compared with those manually traced by a radiologist, used as the reference standard. The two volumetric methods reached excellent agreement (intraclass correlation coefficient, 0.98) without statistical significance (p = 0.42). The average (± SD) accuracy was 99.4% ± 0.14%, and the average Dice overlap coefficient was 93.6% ± 1.7%. The mean processing time for our automated scheme was 1.03 ± 0.13 minutes, whereas that for manual volumetry was 24.0 ± 4.4 minutes (p volumetry based on our automated scheme agreed excellently with reference-standard volumetry, and it required substantially less completion time.

  15. Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

    Science.gov (United States)

    Demirchian, Hovhannes; Nersessian, Armen; Sadeghian, Saeedeh; Sheikh-Jabbari, M. M.

    2018-05-01

    We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017)., 10.1016/j.physletb.2017.07.028]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

  16. A novel biological 'twin-father' temporal paradox of General Relativity in a Gödel universe - Where reproductive biology meets theoretical physics.

    Science.gov (United States)

    Ashrafian, Hutan

    2018-03-01

    Several temporal paradoxes exist in physics. These include General Relativity's grandfather and ontological paradoxes and Special Relativity's Langevin-Einstein twin-paradox. General relativity paradoxes can exist due to a Gödel universe that follows Gödel's closed timelike curves solution to Einstein's field equations. A novel biological temporal paradox of General Relativity is proposed based on reproductive biology's phenomenon of heteropaternal fecundation. Herein, dizygotic twins from two different fathers are the result of concomitant fertilization during one menstrual cycle. In this case an Oedipus-like individual exposed to a Gödel closed timelike curve would sire a child during his maternal fertilization cycle. As a consequence of heteropaternal superfecundation, he would father his own dizygotic twin and would therefore generate a new class of autofraternal superfecundation, and by doing so creating a 'twin-father' temporal paradox. Copyright © 2017 Elsevier Ltd. All rights reserved.

  17. On the Calculation of Quantum Mechanical Ground States from Classical Geodesic Motion on Certain Spaces of Constant Negative Curvature

    CERN Document Server

    Tomaschitz, R

    1989-01-01

    We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are bounded and recurrent in both directions of the time evolution a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schrodinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories.

  18. A new preprocessing parameter estimation based on geodesic active contour model for automatic vestibular neuritis diagnosis.

    Science.gov (United States)

    Ben Slama, Amine; Mouelhi, Aymen; Sahli, Hanene; Manoubi, Sondes; Mbarek, Chiraz; Trabelsi, Hedi; Fnaiech, Farhat; Sayadi, Mounir

    2017-07-01

    The diagnostic of the vestibular neuritis (VN) presents many difficulties to traditional assessment methods This paper deals with a fully automatic VN diagnostic system based on nystagmus parameter estimation using a pupil detection algorithm. A geodesic active contour model is implemented to find an accurate segmentation region of the pupil. Hence, the novelty of the proposed algorithm is to speed up the standard segmentation by using a specific mask located on the region of interest. This allows a drastically computing time reduction and a great performance and accuracy of the obtained results. After using this fast segmentation algorithm, the obtained estimated parameters are represented in temporal and frequency settings. A useful principal component analysis (PCA) selection procedure is then applied to obtain a reduced number of estimated parameters which are used to train a multi neural network (MNN). Experimental results on 90 eye movement videos show the effectiveness and the accuracy of the proposed estimation algorithm versus previous work. Copyright © 2017 Elsevier B.V. All rights reserved.

  19. Computer-aided measurement of liver volumes in CT by means of geodesic active contour segmentation coupled with level-set algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Suzuki, Kenji; Kohlbrenner, Ryan; Epstein, Mark L.; Obajuluwa, Ademola M.; Xu Jianwu; Hori, Masatoshi [Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637 (United States)

    2010-05-15

    Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F{<=}f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less

  20. Computer-aided measurement of liver volumes in CT by means of geodesic active contour segmentation coupled with level-set algorithms

    International Nuclear Information System (INIS)

    Suzuki, Kenji; Kohlbrenner, Ryan; Epstein, Mark L.; Obajuluwa, Ademola M.; Xu Jianwu; Hori, Masatoshi

    2010-01-01

    Purpose: Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. Methods: The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as ''gold standard.''Results: The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F=0.77; p(F≤f)=0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less completion time

  1. Stability and Instability of the Sub-extremal Reissner-Nordström Black Hole Interior for the Einstein-Maxwell-Klein-Gordon Equations in Spherical Symmetry

    Science.gov (United States)

    Van de Moortel, Maxime

    2018-05-01

    We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole—approaching a sub-extremal Reissner-Nordström background fast enough—in presence of a massive and charged scalar field, motivated by the strong cosmic censorship conjecture in that setting: 1. Stability We prove that spherically symmetric characteristic initial data to the Einstein-Maxwell-Klein-Gordon equations approaching a Reissner-Nordström background with a sufficiently decaying polynomial decay rate on the event horizon gives rise to a space-time possessing a Cauchy horizon in a neighbourhood of time-like infinity. Moreover, if the decay is even stronger, we prove that the space-time metric admits a continuous extension to the Cauchy horizon. This generalizes the celebrated stability result of Dafermos for Einstein-Maxwell-real-scalar-field in spherical symmetry. 2. Instability We prove that for the class of space-times considered in the stability part, whose scalar field in addition obeys a polynomial averaged- L 2 (consistent) lower bound on the event horizon, the scalar field obeys an integrated lower bound transversally to the Cauchy horizon. As a consequence we prove that the non-degenerate energy is infinite on any null surface crossing the Cauchy horizon and the curvature of a geodesic vector field blows up at the Cauchy horizon near time-like infinity. This generalizes an instability result due to Luk and Oh for Einstein-Maxwell-real-scalar-field in spherical symmetry. This instability of the black hole interior can also be viewed as a step towards the resolution of the C 2 strong cosmic censorship conjecture for one-ended asymptotically flat initial data.

  2. On the calculation of quantum mechanical ground states from classical geodesic motion on certain spaces of constant negative curvature

    International Nuclear Information System (INIS)

    Tomaschitz, R.

    1989-01-01

    We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are recurrent in both directions of the time evolution t → +∞, t → -∞ a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schroedinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories. (orig.)

  3. Detection of geodesic acoustic mode oscillations, using multiple signal classification analysis of Doppler backscattering signal on Tore Supra

    International Nuclear Information System (INIS)

    Vermare, L.; Hennequin, P.; Gürcan, Ö.D.

    2012-01-01

    This paper presents the first observation of geodesic acoustic modes (GAMs) on Tore Supra plasmas. Using the Doppler backscattering system, the oscillations of the plasma flow velocity, localized between r/a = 0.85 and r/a = 0.95, and with a frequency, typically around 10 kHz, have been observed at the plasma edge in numerous discharges. When the additional heating power is varied, the frequency is found to scale with C s /R. The MUltiple SIgnal Classification (MUSIC) algorithm is employed to access the temporal evolution of the perpendicular velocity of density fluctuations. The method is presented in some detail, and is validated and compared against standard methods, such as the conventional fast Fourier transform method, using a synthetic signal. It stands out as a powerful data analysis method to follow the Doppler frequency with a high temporal resolution, which is important in order to extract the dynamics of GAMs. (paper)

  4. Avoidance of singularities in asymptotically safe Quantum Einstein Gravity

    Energy Technology Data Exchange (ETDEWEB)

    Kofinas, Georgios [Research Group of Geometry, Dynamical Systems and Cosmology, Department of Information and Communication Systems Engineering, University of the Aegean, Karlovassi 83200, Samos (Greece); Zarikas, Vasilios, E-mail: gkofinas@aegean.gr, E-mail: vzarikas@teilam.gr [Department of Electrical Engineering, Theory Division, ATEI of Central Greece, 35100 Lamia (Greece)

    2015-10-01

    New general spherically symmetric solutions have been derived with a cosmological ''constant'' Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.

  5. Avoidance of singularities in asymptotically safe Quantum Einstein Gravity

    Energy Technology Data Exchange (ETDEWEB)

    Kofinas, Georgios [Research Group of Geometry, Dynamical Systems and Cosmology,Department of Information and Communication Systems Engineering,University of the Aegean, Karlovassi 83200, Samos (Greece); Zarikas, Vasilios [Department of Electrical Engineering, Theory Division, ATEI of Central Greece,35100 Lamia (Greece); Department of Physics, Aristotle University of Thessaloniki,54124 Thessaloniki (Greece)

    2015-10-30

    New general spherically symmetric solutions have been derived with a cosmological “constant” Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.

  6. Embedding of the radiation cosmos

    International Nuclear Information System (INIS)

    Wang, J.Z.

    1986-01-01

    The embedding of the Friedmann manifold into a higher dimensional Minkowski space is investigated. As solutions of the Friedmann equation with vanishing cosmological term, Friedmann models describe a first expanding, then contracting universe and predict a big bang singularity. For cosmic time t → 0, R(t) → 0, there is an infinite scalar, curvature in the matter cosmos, and an infinite eigenvalue corresponding to the unique timelike eigenvector of the energy-momentum tensor in the radiation cosmos. The big bang, therefore, is an intrinsic singularity of the space time. To investigate the singularity one resorts to the embedding of the Friedmann manifold into a higher dimensional Minkowski space. For the matter cosmos such an investigation has already been done (Lauro and Schucking, 1984). However, the matter cosmos is not a suitable model to discuss the very early universe where the radiation dominates. Geometric properties, such as the Riemann tensor, the Guassian curvature and the global behavior of the geodesics of the embedded manifold, are discussed in detail

  7. SU-F-R-27: Use Local Shape Descriptor Based On Geodesic Distance to Predict Survival in Non-Small Cell Lung Cancer After Radiotherapy

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, H; Yan, L; Huang, K; Kong, F; Jin, J [Georgia Regents University, Augusta, GA (Georgia)

    2016-06-15

    Purpose: The shape of the Positron Emission Tomography (PET) image represents the heterogeneity of tumor growth in various directions, and thus could be associated with tumor malignancy. We have proposed a median geodesic distance (MGD) to represent the local complexity of the shape and use a normalized MGD (NMGD) to quantify the shape, and found a potential correlation of NMGD to survival in a 20-patient pilot study. This study was to verify the finding in a larger patient cohort. Methods: Geodesic distance of two vertices on a surface is defined as the shortest path on the surface connecting the two vertices. The MGD was calculated for each vertex on the surface to display the local complexity of the shape. The NMGD was determined as: NMGD = 100*standard deviation(MGDs)/mean(MGDs). We applied the NMGD to 40 NSCLC patients who were enrolled in prospective PET image protocols and received radiotherapy. Each patient had a pre-treatment PET scan with the resolution of 4mm*4mm*5mm. Tumors were contoured by a professional radiation oncologist and triangulation meshes were built up based on the contours. Results: The mean and standard deviation of NMGD was 6.4±3.0. The OS was 33.1±16.9 months for low NMGD group, and 15.4±15.6 months for the high NMGD group. The low NMGD group had significant better OS than the high NMGD group (p=0.0013). Conclusion: NMGD could be used as a shape biomarker to predict survival and the MGD could be combined with image texture in future to increase prediction accuracy. This study was supported by Award Number 1R01CA166948 from the NIH and National Cancer Institute.

  8. A rotating string

    International Nuclear Information System (INIS)

    Jensen, B.

    1993-06-01

    The author presents a global solution of Einstein's equations which represents a rotating cosmic string with a finite coreradius. The importance of pressure for the generation of closed timelike curves outside the coreregion of such strings is clearly displayed in this model due to the simplicity of the source. 10 refs

  9. Twisting null geodesic congruences, scri, H-space and spin-angular momentum

    International Nuclear Information System (INIS)

    Kozameh, Carlos; Newman, E T; Silva-Ortigoza, Gilberto

    2005-01-01

    The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat spacetime with a given Bondi shear, one can find (by integrating a partial differential equation) a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences. The class is uniquely given up to the arbitrary choice of a complex analytic world line in a four-parameter complex space. Surprisingly, this parameter space turns out to be the H-space that is associated with the real physical spacetime under consideration. The main development in this work is the demonstration of how this complex world line can be made both unique and also given a physical meaning. More specifically, by forcing or requiring a certain term in the asymptotic Weyl tensor to vanish, the world line is uniquely determined and becomes (by several arguments) identified as the 'complex centre of mass'. Roughly, its imaginary part becomes identified with the intrinsic spin-angular momentum while the real part yields the orbital angular momentum. One should think of this work as developing a generalization of the properties of the algebraically special spacetimes in the sense that the term that is forced here to vanish is automatically vanishing (among many other terms) for all the algebraically special metrics. This is demonstrated in the several given examples. It was, in fact, an understanding of the algebraically special metrics and their associated shear-free null congruence that led us to this construction of the asymptotically shear-free congruences and the unique complex world line. The Robinson-Trautman metrics and the Kerr and charged Kerr metrics with their properties are explicit examples of the construction given here

  10. Global 3-D FDTD Maxwell's-Equations Modeling of Ionospheric Disturbances Associated with Earthquakes Using an Optimized Geodesic Grid

    Science.gov (United States)

    Simpson, J. J.; Taflove, A.

    2005-12-01

    We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A

  11. Cross-code gyrokinetic verification and benchmark on the linear collisionless dynamics of the geodesic acoustic mode

    Science.gov (United States)

    Biancalani, A.; Bottino, A.; Ehrlacher, C.; Grandgirard, V.; Merlo, G.; Novikau, I.; Qiu, Z.; Sonnendrücker, E.; Garbet, X.; Görler, T.; Leerink, S.; Palermo, F.; Zarzoso, D.

    2017-06-01

    The linear properties of the geodesic acoustic modes (GAMs) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, and safety factor), electro-magnetic effects, collisions, and the presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the Lagrangian (particle-in-cell) code ORB5, the Eulerian code GENE, and semi-Lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation.

  12. On vector fields having properties of Reeb fields

    OpenAIRE

    Hajduk, Boguslaw; Walczak, Rafal

    2011-01-01

    We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.

  13. Holographic Protection of Chronology in Universes of the Godel Type

    Energy Technology Data Exchange (ETDEWEB)

    Boyda, Edward; Ganguli, Surya; Horava, Petr; Varadarajan, Uday

    2002-12-07

    We analyze the structure of supersymmetric Godel-like cosmological solutions of string theory. Just as the original four-dimensional Godel universe, these solutions represent rotating, topologically trivial cosmologies with a homogeneous metric and closed timelike curves. First we focus on"phenomenological" aspects of holography, and identify the preferred holographic screens associated with inertial comoving observers in Godel universes. We find that holography can serve as a chronology protection agency: The closed timelike curves are either hidden behind the holographic screen, or broken by it into causal pieces. In fact, holography in Godel universes has many features in common with de Sitter space, suggesting that Godel universes could represent a supersymmetric laboratory for addressing the conceptual puzzles of de Sitter holography. Then we initiate the investigation of"microscopic" aspects of holography of Godel universes in string theory. We show that Godel universes are T-dual to pp-waves, and use this fact to generate new Godel-like solutions of string and M-theory by T-dualizing known supersymmetric pp-wave solutions.

  14. Holographic protection of chronology in universes of the Goedel type

    International Nuclear Information System (INIS)

    Boyda, Edward K.; Ganguli, Surya; Horava, Petr; Varadarajan, Uday

    2003-01-01

    We analyze the structure of supersymmetric Goedel-like cosmological solutions of string theory. Just as the original four-dimensional Goedel universe, these solutions represent rotating, topologically trivial cosmologies with a homogeneous metric and closed timelike curves. First we focus on the 'phenomenological' aspects of holography, and identify the preferred holographic screens associated with inertial comoving observers in Goedel universes. We find that holography can serve as a chronology protection agency: The closed timelike curves are either hidden behind the holographic screen, or broken by it into causal pieces. In fact, holography in Goedel universes has many features in common with de Sitter space, suggesting that Goedel universes could represent a supersymmetric laboratory for addressing the conceptual puzzles of de Sitter holography. Then we initiate the investigation of 'microscopic' aspects of holography of Goedel universes in string theory. We show that Goedel universes are T dual to pp waves, and use this fact to generate new Goedel-like solutions of string and M theory by T dualizing known supersymmetric pp-wave solutions

  15. CT liver volumetry using geodesic active contour segmentation with a level-set algorithm

    Science.gov (United States)

    Suzuki, Kenji; Epstein, Mark L.; Kohlbrenner, Ryan; Obajuluwa, Ademola; Xu, Jianwu; Hori, Masatoshi; Baron, Richard

    2010-03-01

    Automatic liver segmentation on CT images is challenging because the liver often abuts other organs of a similar density. Our purpose was to develop an accurate automated liver segmentation scheme for measuring liver volumes. We developed an automated volumetry scheme for the liver in CT based on a 5 step schema. First, an anisotropic smoothing filter was applied to portal-venous phase CT images to remove noise while preserving the liver structure, followed by an edge enhancer to enhance the liver boundary. By using the boundary-enhanced image as a speed function, a fastmarching algorithm generated an initial surface that roughly estimated the liver shape. A geodesic-active-contour segmentation algorithm coupled with level-set contour-evolution refined the initial surface so as to more precisely fit the liver boundary. The liver volume was calculated based on the refined liver surface. Hepatic CT scans of eighteen prospective liver donors were obtained under a liver transplant protocol with a multi-detector CT system. Automated liver volumes obtained were compared with those manually traced by a radiologist, used as "gold standard." The mean liver volume obtained with our scheme was 1,520 cc, whereas the mean manual volume was 1,486 cc, with the mean absolute difference of 104 cc (7.0%). CT liver volumetrics based on an automated scheme agreed excellently with "goldstandard" manual volumetrics (intra-class correlation coefficient was 0.95) with no statistically significant difference (p(F<=f)=0.32), and required substantially less completion time. Our automated scheme provides an efficient and accurate way of measuring liver volumes.

  16. Computational Analysis of Natural Ventilation Flows in Geodesic Dome Building in Hot Climates

    Directory of Open Access Journals (Sweden)

    Zohreh Soleimani

    2016-08-01

    Full Text Available For centuries, dome roofs were used in traditional houses in hot regions such as the Middle East and Mediterranean basin due to its thermal advantages, structural benefits and availability of construction materials. This article presents the computational modelling of the wind- and buoyancy-induced ventilation in a geodesic dome building in a hot climate. The airflow and temperature distributions and ventilation flow rates were predicted using Computational Fluid Dynamics (CFD. The three-dimensional Reynolds-Averaged Navier-Stokes (RANS equations were solved using the CFD tool ANSYS FLUENT15. The standard k-epsilon was used as turbulence model. The modelling was verified using grid sensitivity and flux balance analysis. In order to validate the modelling method used in the current study, additional simulation of a similar domed-roof building was conducted for comparison. For wind-induced ventilation, the dome building was modelled with upper roof vents. For buoyancy-induced ventilation, the geometry was modelled with roof vents and also with two windows open in the lower level. The results showed that using the upper roof openings as a natural ventilation strategy during winter periods is advantageous and could reduce the indoor temperature and also introduce fresh air. The results also revealed that natural ventilation using roof vents cannot satisfy thermal requirements during hot summer periods and complementary cooling solutions should be considered. The analysis showed that buoyancy-induced ventilation model can still generate air movement inside the building during periods with no or very low wind.

  17. Motion of charged particles in a NUTty Einstein-Maxwell spacetime and causality violation

    Science.gov (United States)

    Clément, Gérard; Guenouche, Mourad

    2018-06-01

    We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner-Nordström-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion.

  18. MALBEC: a new CUDA-C ray-tracer in general relativity

    Science.gov (United States)

    Quiroga, G. D.

    2018-06-01

    A new CUDA-C code for tracing orbits around non-charged black holes is presented. This code, named MALBEC, take advantage of the graphic processing units and the CUDA platform for tracking null and timelike test particles in Schwarzschild and Kerr. Also, a new general set of equations that describe the closed circular orbits of any timelike test particle in the equatorial plane is derived. These equations are extremely important in order to compare the analytical behavior of the orbits with the numerical results and verify the correct implementation of the Runge-Kutta algorithm in MALBEC. Finally, other numerical tests are performed, demonstrating that MALBEC is able to reproduce some well-known results in these metrics in a faster and more efficient way than a conventional CPU implementation.

  19. The regular cosmic string in Born-Infeld gravity

    Energy Technology Data Exchange (ETDEWEB)

    Ferraro, Rafael; Fiorini, Franco, E-mail: ferraro@iafe.uba.ar, E-mail: franco@iafe.uba.ar [Instituto de AstronomIa y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina)

    2011-09-22

    It is shown that Born-Infeld gravity -a high energy deformation of Einstein gravity-removes the singularities of a cosmic string. The respective vacuum solution results to be free of conical singularity and closed timelike curves. The space ends at a minimal circle where the curvature invariants vanish; but this circle cannot be reached in a finite proper time.

  20. Some applications on tangent bundle with Kaluza-Klein metric

    Directory of Open Access Journals (Sweden)

    Murat Altunbaş

    2017-01-01

    Full Text Available In this paper, differential equations of geodesics; parallelism, incompressibility and closeness conditions of the horizontal and complete lift of the vector fields are investigated with respect to Kaluza-Klein metric on tangent bundle.

  1. Boundary singularities produced by the motion of soap films.

    Science.gov (United States)

    Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I

    2014-06-10

    Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

  2. Fixed point theorems in spaces and -trees

    Directory of Open Access Journals (Sweden)

    Kirk WA

    2004-01-01

    Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.

  3. Gödel and Gödel-type universes in Brans–Dicke theory

    Energy Technology Data Exchange (ETDEWEB)

    Agudelo, J.A., E-mail: jaar@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso (Brazil); Nascimento, J.R., E-mail: jroberto@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, Paraíba (Brazil); Petrov, A.Yu., E-mail: petrov@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, Paraíba (Brazil); Porfírio, P.J., E-mail: pporfirio@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, Paraíba (Brazil); Santos, A.F., E-mail: alesandroferreira@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso (Brazil); Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road Victoria, BC (Canada)

    2016-11-10

    In this paper, conditions for existence of Gödel and Gödel-type solutions in Brans–Dicke (BD) scalar–tensor theory and their main features are studied. The consistency of equations of motion, causality violation and existence of CTCs (closed time-like curves) are investigated. The role which cosmological constant and Mach principle play to achieve the consistency of this model is studied.

  4. Radiation from a moving mirror in two dimensional space-time: conformal anomaly

    International Nuclear Information System (INIS)

    Fulling, S.A.; Davies, P.C.W.

    1976-01-01

    The energy-momentum tensor is calculated in the two dimensional quantum theory of a massless scalar field influenced by the motion of a perfectly reflecting boundary (mirror). The simple model system evidently can provide insight into more sophisticated processes, such as particle production in cosmological models and exploding black holes. In spite of the conformally static nature of the problem, the vacuum expectation value of the tensor for an arbitrary mirror trajectory exhibits a non-vanishing radiation flux (which may be readily computed). The expectation value of the instantaneous energy flux is negative when the proper acceleration of the mirror is increasing, but the total energy radiated during a bounded mirror motion is positive. A uniformly accelerating mirror does not radiate; however, the quantization does not coincide with the treatment of that system as a 'static universe'. The calculation of the expectation value requires a regularization procedure of covariant separation of points (in products of field operators) along time-like geodesics; more naive methods do not yield the same answers. A striking example involving two mirrors clarifies the significance of the conformal anomaly. (author)

  5. Stationary strings near a higher-dimensional rotating black hole

    International Nuclear Information System (INIS)

    Frolov, Valeri P.; Stevens, Kory A.

    2004-01-01

    We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D (five-dimensional) Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration that crosses the infinite redshift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole, there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a space-time with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string

  6. The preparation problem in nonlinear extensions of quantum theory

    OpenAIRE

    Cavalcanti, Eric G.; Menicucci, Nicolas C.; Pienaar, Jacques L.

    2012-01-01

    Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationa...

  7. Holography in Goedel-type spacetimes and their generalizations

    Energy Technology Data Exchange (ETDEWEB)

    Klepac, P [Inst. Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 611 37 Brno (Czech Republic)

    2006-03-01

    In the contribution we review some facts concerning holography in the Godel-type universes, adopting the approach presented in the paper Boyda at all. Then the analysis is extended to an inhomogeneous cylindrically symmetric solution, found in framework of Einstein-Maxwell-dilaton gravity, which violates the causality. In particular, the question is raised, whether holographic screens shield the closed timelike curves from an observer, thus providing a chronology protection mechanism.

  8. General relativistic model of a spinning cosmic string

    International Nuclear Information System (INIS)

    Jensen, B.; Soleng, H.H.

    1991-11-01

    The authors investigate the infinite, straight, rotating cosmic string within the framework of Einstein's General Theory of Relativity. A class of exact interior solutions is derived for which the source satisfies the weak and the dominant energy conditions. The interior metric is matched smoothly to the exterior vacuum. A subclass of these solutions has closed time-like curves both in the interior and the exterior geometry. 39 refs., 2 figs

  9. Ricci time in the Lemaître-Tolman model and the block universe

    Science.gov (United States)

    Elmahalawy, Yasser; Hellaby, Charles; Ellis, George F. R.

    2015-10-01

    It is common to think of our universe according to the "block universe" concept, which says that spacetime consists of many "stacked" three-surfaces, labelled by some kind of proper time, . Standard ideas do not distinguish past and future, but Ellis' "evolving block universe" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. This work investigates the shape of the "Ricci time" surfaces relative to the the null surfaces. We use the Lemaître-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these constant surfaces, , to be spacelike or timelike. Furthermore, we look at the effect of strong gravity domains by determining the location of timelike S regions relative to apparent horizons. We find that constant Ricci time surfaces are always spacelike near the big bang, while at late times (near the crunch or the extreme far future), they are only timelike under special circumstances. At intermediate times, timelike S regions are common unless the variation of the bang time is restricted. The regions where these surfaces become timelike are often adjacent to apparent horizons, but always outside them, and in particular timelike S regions do not occur inside the horizons of black-hole-like models.

  10. On the asymptotic behavior of complex earthquakes and Teichmüller disks

    DEFF Research Database (Denmark)

    Gupta, Subhojoy

    2015-01-01

    Given a hyperbolic surface and a simple closed geodesic on it, complex-twists along the curve produce a holomorphic family of deformations in Teichmuller space, degenerating to the Riemann surface where it is pinched. We show there is a corresponding Teichmuller disk such that the two are strongl...

  11. Thermodynamic and multifractal formalism and the Bowen-series map

    International Nuclear Information System (INIS)

    Rudolph, O.

    1995-01-01

    In the theory of quantum chaos one studies the semiclassical behaviour of quantum mechanical systems whose corresponding classical counterparts exhibit chaos. The geodesic motion of a free classical particle on closed Riemann surfaces with constant negative curvature is strongly chaotic. Selberg's theory relates the classical and the quantum mechanical systems. These systems are sometimes considered as model systems in the theory of quantum chaos since they are well understood from a mathematical point of view. In this work we study the multifractal formalism for the geodesic flow on surfaces with constant negative curvature. The multifractal analysis of measures has been developed in order to characterize the scaling behaviour of measures on attractors of classical chaotic dynamical systems globally. In order to relate the multifractal formalism with quantities usually considered in the study of the geodesic flow on Riemann surfaces with constant negative curvature, it is necessary to establish the assertions of the multifractal formalism in a mathematically rigorous way. This is achieved with the help of the thermodynamic formalism for hyperbolic dynamical systems developed by Ruelle, Bowen and others. (orig.)

  12. Cosmic censorship, black holes, and particle orbits

    International Nuclear Information System (INIS)

    Hiscock, W.A.

    1979-01-01

    One of the main reasons for believing in the cosmic censorship hypothesis is the disquieting nature of the alternative: the existence of naked singularities, and hence loss of predictability, the possibility of closed timelike lines and so forth. The consequences of assuming the cosmic hypothesis can also be somewhat strange and unexpected. In particular, Hawking's black hole area theorem is applied to the study of particle orbits near a Schwarzschild black hole. If the cosmic censorship hypothesis (and hence the area theorem) is true, then there exist stable near-circular orbits arbitrarily close to the horizon at r = 2M. (author)

  13. Gravitational redshift from a binary system

    Energy Technology Data Exchange (ETDEWEB)

    Steklain, Andre [Universidade Tecnologica Federal do Parana (UTFPR), PR (Brazil)

    2011-07-01

    Full text: In this work we study the gravitational redshift of a binary system in general relativity. We employ a mixed metric obtained from the matching of a 1PN metric with two perturbed Schwarzschild metrics, based on previous works [Alvi, Phys. Rev. D, 61, 124013 (2000)]. This metric is well known, and has been considered for several applications [Steklain et al, Phys. Lett. A, 373, 188, (2009)]. We consider a massless observer in a timelike geodesic of this metric measuring the redshift of the system. The observer concentrates the redshift measurements in one of the massive bodies and is influenced by the mass of the second body. We find that there is a substantial contribution of the second mass in some cases. We compare with experimental data obtained for real binary systems of white dwarfs [Vennes et al, Astroph. J., L37 (1991)]. We also discuss these results for more massive systems, and make some predictions for very massive systems, like black holes, although it extrapolates the limit of the 1PN approximation used. Is well known that the major contribution of the observed redshift is from the universe expansion, but these results indicate that the influence of the gravitational redshift may be underestimated at some systems. (author)

  14. From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity

    Directory of Open Access Journals (Sweden)

    Rami Ahmad El-Nabulsi

    2015-08-01

    Full Text Available Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein’s field equations yet the gravity is discretized and originated from “spacetime discreteness”. A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.

  15. Optimal time travel in the Godel universe

    OpenAIRE

    Natario, Jose

    2011-01-01

    Using the theory of optimal rocket trajectories in general relativity, recently developed in arXiv:1105.5235, we present a candidate for the minimum total integrated acceleration closed timelike curve in the Godel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament's conjectured value (Malament, 1984), as was already implicit in the work of Manchak (Manchak, 2011); however, Malament's conjecture does seem to hold for periodic ...

  16. Renormalization-group flows and charge transmutation in string theory

    International Nuclear Information System (INIS)

    Orlando, D.; Petropoulos, P.M.; Sfetsos, K.

    2006-01-01

    We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an attractor from both the target-space and world-sheet points of view. We also address the question of instabilities created by the presence of closed time-like curves in string backgrounds. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  17. Numerical calculations near spatial infinity

    International Nuclear Information System (INIS)

    Zenginoglu, Anil

    2007-01-01

    After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field equations based on the conformal Gauss gauge allow us in spherical symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in a smooth way including spacelike, null and timelike infinity and the domain close to the singularity

  18. On the dynamics of second-order Lagrangian systems

    Directory of Open Access Journals (Sweden)

    Ronald Adams

    2017-04-01

    Full Text Available In this article we are concerned with improving the twist condition for second-order Lagrangian systems. We characterize a local Twist property and demonstrate how results on the existence of simple closed characteristics can be extended in the case of the Swift-Hohenberg / extended Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution equations for broken geodesic curves that could be used to investigate more general systems or closed characteristics.

  19. Gödel metrics with chronology protection in Horndeski gravities

    Science.gov (United States)

    Geng, Wei-Jian; Li, Shou-Long; Lü, H.; Wei, Hao

    2018-05-01

    Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein-Horndeski gravity. We construct such exact solutions also in Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.

  20. Liouville's equation and radiative acceleration in general relativity

    International Nuclear Information System (INIS)

    Keane, A.J.

    1999-01-01

    spacetimes. In the case of the Schwarzschild spacetime we find a solution of the Liouville equation which is invariant under the Killing vector symmetries and we adopt this as our model radiation field. Once a particular solution has been chosen the radiation field has been specified completely throughout the spacetime. In chapter 4 we investigate null and timelike geodesics in the Schwarzschild spacetime. Studying the null geodesics allows us to determine the viewing angles, that is, the (semi) angular size of the compact object as viewed by a stationary observer at an arbitrary point in the spacetime. The timelike geodesics are the trajectories of the (massive) test particles subject to no external radiation force and therefore constitute a limiting case of the radiative acceleration results. Given the radiation field one can calculate the radiation pressure force and because of special relativistic effects, the radiation pressure force experienced by the particle becomes velocity dependent. In chapter 5 we integrate the equations of motion for the case of purely radial motion in the Thomson limit. In this case we can obtain a tractable analytic expression for the solution in phase space, which can be compared with the high frequency case. In this chapter we consider a relativistic critical luminosity of a compact object, i.e. a relativistic Eddington luminosity. We also introduce and discuss terminal velocities and saturation velocities associated with a particular compact object. The terminal velocity of a radiation field is the 3-velocity required to annul the radiation pressure force on the test particle, neglecting the influence of any gravitational force on the particle. The saturation velocity is defined in the same way except the gravitational force is included. The saturation velocities are of course highly frequency dependent and provide important information about the dynamics of the system. In chapter 6 we discuss the Compton differential cross-section for

  1. Meson-exchange enhancement of the first forbidden $0^{+} \\leftrightarrow 0^{-} \\beta$-transitions

    CERN Multimedia

    2002-01-01

    In the frame of the standard model of the weak interaction, it has been suggested by Kubodera, Delorme and Rho, that pion exchange should have a large effect on the rank-zero time-like component of the axial current A$_{0}$. The best case for the study of A$ _{0}$ is $0^{-} \\leftrightarrow 0^{+} \\beta$-decay since in this process only rank zero matrix elements of the time-like and space-like components of the axial current contribute to the transition rate. $0^{-} \\leftrightarrow 0^{+}$ decays have been studied in the vicinity of doubly closed-shell nuclei such as $^{16}$O, $^{96}$Zr, and $^{208}$Pb where s$_{1/2} \\leftrightarrow$ p$_{1/2}$ matrix elements were involved. In these cases, the meson-exchange correction to the one-body axial-charge density is significant. ISOLDE offers the possibility to perform sensitive measurements of the $0^{-} \\leftrightarrow 0^{+}$ pseudoscalar decay in nuclei where the p$_{3/2} \\rightarrow$ d$_{3/2}$ matrix elements are involved. We therefore propose a search of the $^{38}...

  2. On extracting physical content from asymptotically flat spacetime metrics

    International Nuclear Information System (INIS)

    Kozameh, C; Newman, E T; Silva-Ortigoza, G

    2008-01-01

    A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g. degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates), or from solutions that have symmetries or approximate symmetries. In the present work, we will be concerned with asymptotically flat spacetimes where the approximate symmetry is the Bondi-Metzner-Sachs group. For these spaces the Bondi 4-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat spacetimes, we give kinematic meaning to the Bondi 4-momentum. In other words, we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux

  3. Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy

    KAUST Repository

    Majumdar, Apala

    2009-10-01

    Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we evaluate the infimum Dirichlet energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1, ..., sn}, *). These results have applications for the theoretical modelling of nematic liquid crystal devices. To cite this article: A. Majumdar et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.

  4. Tunnelling from Goedel black holes

    International Nuclear Information System (INIS)

    Kerner, Ryan; Mann, R. B.

    2007-01-01

    We consider the spacetime structure of Kerr-Goedel black holes, analyzing their parameter space in detail. We apply the tunnelling method to compute their temperature and compare the results to previous calculations obtained via other methods. We claim that it is not possible to have the closed timelike curve (CTC) horizon in between the two black hole horizons and include a discussion of issues that occur when the radius of the CTC horizon is smaller than the radius of both black hole horizons

  5. Bel-Robinson energy and the nature of singularities in isotropic cosmologies

    International Nuclear Information System (INIS)

    Klaoudatou, Ifigeneia; Cotsakis, Spiros

    2007-01-01

    We review our recent work on the classification of finite time singularities that arise in isotropic universes. This scheme is based on the exploitation of the Bel Robinson energy in a cosmological setting. We comment on the relation between geodesic completeness and the Bel Robinson energy and present evidence that relates the divergence of the latter to the existence of closed trapped surfaces

  6. On an isospectrality question over compact Riemann surfaces

    International Nuclear Information System (INIS)

    Srinivas Rau, S.

    1990-01-01

    It is proved that for a generic compact Riemann surface X of genus g>1,(i) there are at most 2 2g unitary characters of π 1 (X) whose associated line bundles have laplacians of identical spectrum, (ii) generating cycles for π 1 (X) can be chosen to be closed geodesics whose length multiplicity is 1. (author). 5 refs

  7. Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

    Science.gov (United States)

    Gong, Yungui; Hou, Shaoqi; Liang, Dicong; Papantonopoulos, Eleftherios

    2018-04-01

    In this work we discuss the polarization contents of Einstein-æther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-æther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-æther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-æther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

  8. Ray trajectories for a spinning cosmic string and a manifestation of self-cloaking

    International Nuclear Information System (INIS)

    Anderson, Tom H.; Mackay, Tom G.; Lakhtakia, Akhlesh

    2010-01-01

    A study of ray trajectories was undertaken for the Tamm medium which represents the spacetime of a zero-tension cosmic spinning string, under the geometric-optics approximation. Our numerical studies revealed that: (i) rays never cross the string's boundary; (ii) the Tamm medium supports evanescent waves in regions of phase space that correspond to those regions of the string's spacetime which could support closed timelike curves; and (iii) a spinning string can be slightly visible while a non-spinning string is almost perfectly invisible.

  9. On H-closed and U-closed functions | Cammaroto | Quaestiones ...

    African Journals Online (AJOL)

    In this article, we extend the work on H-closed functions started by Cammaroto, Fedorchuk and Porter in 1998. Also, U-closed functions are introduced and characterized in terms of filters and adherence. The hereditary and productivity properties are examined and developed for both H-closed and U-closed functions.

  10. Generalized Kerr spacetime with an arbitrary mass quadrupole moment: geometric properties versus particle motion

    International Nuclear Information System (INIS)

    Bini, Donato; Geralico, Andrea; Luongo, Orlando; Quevedo, Hernando

    2009-01-01

    An exact solution of Einstein's field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with an arbitrary mass quadrupole moment and is specified by three parameters, the mass M, the angular momentum per unit mass a and the quadrupole parameter q. It reduces to the Kerr spacetime in the limiting case q = 0 and to the Erez-Rosen spacetime when the specific angular momentum a vanishes. The geometrical properties of such a solution are investigated. Causality violations, directional singularities and repulsive effects occur in the region close to the source. Geodesic motion and accelerated motion are studied on the equatorial plane which, due to the reflection symmetry property of the solution, also turns out to be a geodesic plane.

  11. Automatic closed-loop stereo-photogrammetric system for the Nuclear Power Station Paks

    International Nuclear Information System (INIS)

    Eoery, K.; Szabados, J.; Szerovay, A.

    1982-01-01

    The geodesic work for the NPS Paks project required an extensive modernization of traditional measuring techniques, besides the development of measuring devices and methods encompassing the complete procedure of data processing. Stereo-photogrammetry based on three-dimensional measuring technique plays an outstanding role in 'bulk work' required for measuring as well as in efficient technical data supply. A detailed analysis of the technical parameters is given concerning the interactive graphic and digital data processing and data base organizing system. After the description of the main types of process equipment system organization problems are discussed. The paper outlines research and testing tasks related to the practical application of the technology system of world standard, representing a unique solution in Hungarian relation. Finally, fields of application for the system in power station design are presented. (author)

  12. Hyperbolic strings

    International Nuclear Information System (INIS)

    Popov, A.D.

    1991-01-01

    We introduce hyperbolic strings as closed bosonic strings with the target space R d-1,1 xT q+1,1 which has an additional time-like dimension in the internal space. The Fock spaces of the q-parametric family of standard bosonic, fermionic and heterotic strings with the target spaces of dimension n≤d+q are shown to be embedded into the Fock space of hyperbolic strings. The condition of the absence of anomaly fixes d and q for all three types of strings written in a bosonized form. (orig.)

  13. A new approach to spherically symmetric junction surfaces and the matching of FLRW regions

    International Nuclear Information System (INIS)

    Kirchner, U

    2004-01-01

    We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann-LemaItre-Robertson-Walker (FLRW) models. We discuss 'vacuum bubbles' and closed-open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time

  14. Interactive visualization of a thin disc around a Schwarzschild black hole

    International Nuclear Information System (INIS)

    Müller, Thomas; Frauendiener, Jörg

    2012-01-01

    In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a Schwarzschild black hole can be determined interactively by means of an analytic solution to the geodesic equation processed on current high-performance graphical processing units. This approach can, in principle, be customized for any other thin disc in a spacetime with geodesics given in closed form. The interactive visualization discussed here can be used either in a first course in general relativity for demonstration purposes only or as a thesis for an enthusiastic student in an advanced course with some basic knowledge of OpenGL and a programming language. (paper)

  15. A note on stable Teichmüller quasigeodesics

    Indian Academy of Sciences (India)

    Abstract. In this note, we prove that for a cobounded, Lipschitz path γ : I → T in the Teichmüller space T of a hyperbolic surface, if the pull back bundle Hγ → I of the cannonical H2-bundle H → T is a strongly relatively hyperbolic metric space then there exists a geodesic ξ of T such that γ(I) and ξ are close to each other.

  16. Non-Abelian, supersymmetric black holes and strings in 5 dimensions

    International Nuclear Information System (INIS)

    Meessen, Patrick; Ortín, Tomás; Ramírez, Pedro F.

    2016-01-01

    We construct and study the first supersymmetric black-hole and black-string solutions of non-Abelian-gauged N=1,d=5 supergravity (N=1,d=5 Super-Einstein-Yang-Mills theory) with non-trivial SU(2) gauge fields: BPST instantons for black holes and BPS monopoles of different kinds (’t Hooft-Polyakov, Wu-Yang and Protogenov) for black strings and also for certain black holes that are well defined solutions only for very specific values of all the moduli. Instantons, as well as colored monopoles do not contribute to the masses and tensions but do contribute to the entropies. The construction is based on the characterization of the supersymmetric solutions of gauged N=1,d=5 supergravity coupled to vector multiplets achieved in ref. http://dx.doi.org/10.1088/1126-6708/2007/08/096 which we elaborate upon by finding the rules to construct supersymmetric solutions with one additional isometry, both for the timelike and null classes. These rules automatically connect the timelike and null non-Abelian supersymmetric solutions of N=1,d=5 SEYM theory with the timelike ones of N=2,d=4 SEYM theory http://dx.doi.org/10.1103/PhysRevD.78.065031; http://dx.doi.org/10.1088/1126-6708/2008/09/099 by dimensional reduction and oxidation. In the timelike-to-timelike case the singular Kronheimer reduction recently studied in ref. http://dx.doi.org/10.1016/j.physletb.2015.04.065 plays a crucial role.

  17. Axially symmetric Lorentzian wormholes in general relativity

    International Nuclear Information System (INIS)

    Schein, F.

    1997-11-01

    The field equations of Einstein's theory of general relativity, being local, do not fix the global structure of space-time. They admit topologically non-trivial solutions, including spatially closed universes and the amazing possibility of shortcuts for travel between distant regions in space and time - so-called Lorentzian wormholes. The aim of this thesis is to (mathematically) construct space-times which contain traversal wormholes connecting arbitrary distant regions of an asymptotically flat or asymptotically de Sitter universe. Since the wormhole mouths appear as two separate masses in the exterior space, space-time can at best be axially symmetric. We eliminate the non-staticity caused by the gravitational attraction of the mouths by anchoring them by strings held at infinity or, alternatively, by electric repulsion. The space-times are obtained by surgically grafting together well-known solutions of Einstein's equations along timelike hypersurfaces. This surgery naturally concentrates a non-zero stress-energy tensor on the boundary between the two space-times which can be investigated by using the standard thin shell formalism. It turns out that, when using charged black holes, the provided constructions are possible without violation of any of the energy conditions. In general, observers living in the axially symmetric, asymptotically flat (respectively asymptotically de Sitter) region axe able to send causal signals through the topologically non-trivial region. However, the wormhole space-times contain closed timelike curves. Because of this explicit violation of global hyperbolicity these models do not serve as counterexamples to known topological censorship theorems. (author)

  18. Surface current equilibria from a geometric point of view

    International Nuclear Information System (INIS)

    Kaiser, R.; Salat, A.

    1993-04-01

    This paper addresses the inverse problem of the existence of surface current MHD equilibria in toroidal geometry with vanishing magnetic field inside. Inverse means that the plasma-vacuum interface rather than the external wall or conductors are given and the latter remain to be determined. This makes a reformulation of the problem possible in geometric terms: What toroidal surfaces with analytic parameterization allow a simple analytic covering by geodesics? If such a covering by geodesics (field lines) exists, their orthogonal trajectories (current lines) also form a simple covering and are described by a function satisfying a nonlinear partial differential equation of the Hamilton-Jacobi type whose coefficients are combinations of the metric elements of the surface. All known equilibria - equilibria with zero and infinite rotational transform and the symmetric ones in the case of finite rotational transform - turn out to be solutions of separable cases of that equation and allow a unified description if the toroidal surface is parametrized in the moving trihedral associated with a closed curve. Analogously to volume current equilibria, the only continuous symmetries compatible with separability are plane, helical and axial symmetry. In the nonseparable case numerical evidence is presented for cases with chaotic behaviour of geodesics, thus restricting possible equilibria for these surfaces. For weak deviation from axisymmetry KAM-type behaviour is observed, i.e. destruction of geodesic coverings with a low rational rotational transform and preservation of those with irrational rotational transform. A previous attempt to establish three-dimensional surface current equilibria on the basis of the KAM theorem is rejected as incomplete, and a complete proof of the existence of equilibria in the weakly nonaxisymmetric case, based on the twist theorem for mappings, is given. Finally, for a certain class of strong deviations from axisymmetry an analytic criterion is

  19. The G2 spinorial geometry of supersymmetric IIB backgrounds

    International Nuclear Information System (INIS)

    Gran, U; Gutowski, J; Papadopoulos, G

    2006-01-01

    We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G 2 in Spin(9, 1) x U(1). We find that such backgrounds admit a timelike Killing vector field and the geometric structure of the spacetime reduces from Spin(9, 1) x U(1) to G 2 . We determine the type of G 2 structure that the spacetime admits by computing the covariant derivatives of the spacetime forms associated with the Killing spinor bilinears. We also solve the Killing spinor equations of backgrounds with two supersymmetries and Spin(7) x R 8 -invariant spinors, and four supersymmetries with SU(4) x R 8 - and with G 2 -invariant spinors. We show that the Killing spinor equations factorize in two sets, one involving the geometry and the 5-form flux, and the other the 3-form flux and the scalars. In the Spin(7) x R 8 and SU(4) x R 8 cases, the spacetime admits a parallel null vector field and so the spacetime metric can be locally described in terms of Penrose coordinates adapted to the associated rotation free, null, geodesic congruence. The transverse space of the congruence is a Spin(7) and a SU(4) holonomy manifold, respectively. In the G 2 case, all the fluxes vanish and the spacetime is the product of a three-dimensional Minkowski space with a holonomy G 2 manifold

  20. Towards the proof of the cosmic censorship hypothesis

    Energy Technology Data Exchange (ETDEWEB)

    Krolak, Andrzej

    1986-05-01

    An attempt is made to formulate the cosmic censorship hypothesis put forward by Penrose (1969, Riv. Nuovo Cimento Ser. 1 Num. Spec. 1 252) as a theorem which could be subject to mathematical proof. It is proved that a weakly asymptotically simple and empty spacetime must be future asymptotically predictable if the energy and the strong causality conditions hold and either all singularities are of Tipler's strong curvature type and once singularity occurs there exists a marginally outgoing null geodesic or each singularity is preceded by the occurrence of a closed trapped surface. The marginally outgoing null geodesics may not be admitted by general naked singularities. However, it is shown that they occur if on the Cauchy horizon the global hyperbolicity in violated is such a way that causal simplicity does not hold. This means that a wide class of nakedly singular spacetimes is considered. This result gives some support to the validity of Penrose's hypothesis.

  1. Towards the proof of the cosmic censorship hypothesis

    International Nuclear Information System (INIS)

    Krolak, Andrzej

    1986-01-01

    An attempt is made to formulate the cosmic censorship hypothesis put forward by Penrose [1969, Riv. Nuovo Cimento Ser. 1 Num. Spec. 1 252] as a theorem which could be subject to mathematical proof. It is proved that a weakly asymptotically simple and empty spacetime must be future asymptotically predictable if the energy and the strong causality conditions hold and either all singularities are of Tipler's strong curvature type and once singularity occurs there exists a marginally outgoing null geodesic or each singularity is preceded by the occurrence of a closed trapped surface. The marginally outgoing null geodesics may not be admitted by general naked singularities. However, it is shown that they occur if on the Cauchy horizon the global hyperbolicity in violated is such a way that causal simplicity does not hold. This means that a wide class of nakedly singular spacetimes is considered. This result gives some support to the validity of Penrose's hypothesis. (author)

  2. Visual Analytics for Exploration of a High-Dimensional Structure

    Science.gov (United States)

    2013-04-01

    5 Figure 3. Comparison of Euclidean vs. geodesic distance. LDRs use ...manifold, whereas an LDR fails. ...........................6 Figure 4. WEKA GUI for data mining HDD using FRFS-ACO...of Euclidean vs. geodesic distance. LDRs use metrics based on the Euclidean distance between two points, while the NLDRs are based on geodesic

  3. On the absence of McShane-type identities for the outer space

    OpenAIRE

    Kapovich, Ilya; Rivin, Igor

    2008-01-01

    A remarkable result of McShane states that for a punctured torus with a complete finite volume hyperbolic metric we have \\[ \\sum_{\\gamma} \\frac{1}{e^{\\ell(\\gamma)}+1}={1/2} \\] where $\\gamma$ varies over the homotopy classes of essential simple closed curves and $\\ell(\\gamma)$ is the length of the geodesic representative of $\\gamma$. We prove that there is no reasonable analogue of McShane's identity for the Culler-Vogtmann outer space of a free group.

  4. Is the shell-focusing singularity of Szekeres space-time visible?

    International Nuclear Information System (INIS)

    Nolan, Brien C; Debnath, Ujjal

    2007-01-01

    The visibility of the shell-focusing singularity in Szekeres space-time--which represents quasispherical dust collapse--has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second nonparallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaitre-Tolman-Bondi space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for nonradial null geodesics in the axially symmetric case and in the general (nonaxially symmetric) case, and suggest a possible approach

  5. Principal Curves on Riemannian Manifolds.

    Science.gov (United States)

    Hauberg, Soren

    2016-09-01

    Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

  6. The analytic value of a 3-loop sunrise graph in a particular kinematical configuration

    International Nuclear Information System (INIS)

    Mastrolia, P.; Remiddi, E.

    2003-01-01

    We consider the scalar integral associated to the 3-loop sunrise graph with a massless line, two massive lines of equal mass M, a fourth line of mass equal to Mx, and the external invariant timelike and equal to the square of the fourth mass. We write the differential equation in x satisfied by the integral, expand it in the continuous dimension d around d=4 and solve the system of the resulting chained differential equations in closed analytic form, expressing the solutions in terms of harmonic polylogarithms. As a byproduct, we give the limiting values of the coefficients of the (d-4) expansion at x=1 and x=0

  7. Behaviour and design considerations for continuous flow closed-open-closed liquid microchannels.

    Science.gov (United States)

    Melin, Jessica; van der Wijngaart, Wouter; Stemme, Göran

    2005-06-01

    This paper introduces a method of combining open and closed microchannels in a single component in a novel way which couples the benefits of both open and closed microfluidic systems and introduces interesting on-chip microfluidic behaviour. Fluid behaviour in such a component, based on continuous pressure driven flow and surface tension, is discussed in terms of cross sectional flow behaviour, robustness, flow-pressure performance, and its application to microfluidic interfacing. The closed-open-closed microchannel possesses the versatility of upstream and downstream closed microfluidics along with open fluidic direct access. The device has the advantage of eliminating gas bubbles present upstream when these enter the open channel section. The unique behaviour of this device opens the door to applications including direct liquid sample interfacing without the need for additional and bulky sample tubing.

  8. How many 'times' do we have in quantum gravity?

    International Nuclear Information System (INIS)

    Hosoya, Akio; Soda, Jiro.

    1990-07-01

    Apparently, there are infinite number of time-like variables in the Wheeler-DeWitt equation in quantum gravity. This gives rise to an obvious conceptual difficulty and further becomes an obstacle if one wants to canonically third quantize the universe. In this paper, adopting York's gauge in the path-integral approach, we formulate quantum geometrodynamics so that it contains only a single time-like variable corresponding to the total volume of the universe. (author)

  9. Geometric subspace updates with applications to online adaptive nonlinear model reduction

    DEFF Research Database (Denmark)

    Zimmermann, Ralf; Peherstorfer, Benjamin; Willcox, Karen

    2018-01-01

    In many scientific applications, including model reduction and image processing, subspaces are used as ansatz spaces for the low-dimensional approximation and reconstruction of the state vectors of interest. We introduce a procedure for adapting an existing subspace based on information from...... Estimation (GROUSE). We establish for GROUSE a closed-form expression for the residual function along the geodesic descent direction. Specific applications of subspace adaptation are discussed in the context of image processing and model reduction of nonlinear partial differential equation systems....

  10. Measurement of repeat effects in Chicago’s criminal social network

    Directory of Open Access Journals (Sweden)

    Paul Kump

    2016-07-01

    Full Text Available The “near-repeat” effect is a well-known criminological phenomenon in which the occurrence of a crime incident gives rise to a temporary elevation of crime risk within close physical proximity to an initial incident. Adopting a social network perspective, we instead define a near repeat in terms of geodesic distance within a criminal social network, rather than spatial distance. Specifically, we report a statistical analysis of repeat effects in arrest data for Chicago during the years 2003–2012. We divide the arrest data into two sets (violent crimes and other crimes and, for each set, we compare the distributions of time intervals between repeat incidents to theoretical distributions in which repeat incidents occur only by chance. We first consider the case of the same arrestee participating in repeat incidents (“exact repeats” and then extend the analysis to evaluate repeat risks of those arrestees near one another in the social network. We observe repeat effects that diminish as a function of geodesic distance and time interval, and we estimate typical time scales for repeat crimes in Chicago.

  11. Pipe closing device

    International Nuclear Information System (INIS)

    Klahn, F.C.; Nolan, J.H.; Wills, C.

    1979-01-01

    The closing device closes the upper end of a support tube for monitoring samples. It meshes with the upper connecting piece of the monitorung sample capsule, and loads the capsule within the bore of the support tube, so that it is fixed but can be released. The closing device consists of an interlocking component with a chamber and several ratchets which hang down. The interlocking component surrounds the actuating component for positioning the ratchets. The interlocking and actuating components are movable axially relative to each other. (DG) [de

  12. Inertial forces and the foundations of optical geometry

    International Nuclear Information System (INIS)

    Jonsson, Rickard

    2006-01-01

    Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in general relativity. Inspired by the works of Abramowicz et al (see e.g. Abramowicz and Lasota 1997 Class. Quantum Grav. 14 A23-30), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory have been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference congruence is shearing), appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon always follows a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61). For the particular case when the shear tensor vanishes, we present the inertial force equation in a three-dimensional form (using the bold-face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen and co-workers (see e.g. Bini et al 1997 Int. J. Mod. Phys. D 6 143-98)

  13. Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

    Science.gov (United States)

    Thornburg, Jonathan

    2007-01-01

    Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well

  14. Kaluza-Klein theories and the signature of space-time

    International Nuclear Information System (INIS)

    Aref'eva, I.Ya.; Volovich, I.V.

    1985-06-01

    Higher-dimensional Kaluza-Klein theories with extra compactified time-like variables are considered. Topological criteria are presented for a compact manifold which prevent the appearance of massless ghosts in an effective four-dimensional theory. Some models are given in which these criteria hold. Among them is the bosonic sector of the low-energy limit of the anomaly-free superstring theories. As a rule, the extra time-like variables lead to compactification with a compact hyperbolic manifold. (author)

  15. On static and radiative space-times

    International Nuclear Information System (INIS)

    Friedrich, H.

    1988-01-01

    The conformal constraint equations on space-like hypersurfaces are discussed near points which represent either time-like or spatial infinity for an asymptotically flat solution of Einstein's vacuum field equations. In the case of time-like infinity a certain 'radiativity condition' is derived which must be satisfied by the data at that point. The case of space-like infinity is analysed in detail for static space-times with non-vanishing mass. It is shown that the conformal structure implied here on a slice of constant Killing time, which extends analytically through infinity, satisfies at spatial infinity the radiativity condition. Thus to any static solution exists a certain 'radiative solution' which has a smooth structure at past null infinity and is regular at past time-like infinity. A characterization of these solutions by their 'free data' is given and non-symmetry properties are discussed. (orig.)

  16. Next-to-next-to-leading order evolution of non-singlet fragmentation functions

    International Nuclear Information System (INIS)

    Mitov, A.; Moch, S.; Vogt, A.

    2006-04-01

    We have investigated the next-to-next-to-leading order (NNLO) corrections to inclusive hadron production in e + e - annihilation and the related parton fragmentation distributions, the 'time-like' counterparts of the 'space-like' deep-inelastic structure functions and parton densities. We have re-derived the corresponding second-order coefficient functions in massless perturbative QCD, which so far had been calculated only by one group. Moreover we present, for the first time, the third-order splitting functions governing the NNLO evolution of flavour non-singlet fragmentation distributions. These results have been obtained by two independent methods relating time-like quantities to calculations performed in deep-inelastic scattering. We briefly illustrate the numerical size of the NNLO corrections, and make a prediction for the difference of the yet unknown time-like and space-like splitting functions at the fourth order in the strong coupling constant. (Orig.)

  17. School Closings in Philadelphia

    Science.gov (United States)

    Jack, James; Sludden, John

    2013-01-01

    In 2012, the School District of Philadelphia closed six schools. In 2013, it closed 24. The closure of 30 schools has occurred amid a financial crisis, headlined by the district's $1.35 billion deficit. School closures are one piece of the district's plan to cut expenditures and close its budget gap. The closures are also intended to make…

  18. Generalizing optical geometry

    International Nuclear Information System (INIS)

    Jonsson, Rickard; Westman, Hans

    2006-01-01

    We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

  19. Spacetime completeness of non-singular black holes in conformal gravity

    Energy Technology Data Exchange (ETDEWEB)

    Bambi, Cosimo; Rachwał, Lesław [Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai (China); Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com [Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Road, Shenzhen 518055 (China)

    2017-05-01

    We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new types of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r =0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.

  20. Teichmueller motion of (2+1)-dimensional gravity with the cosmological constant

    International Nuclear Information System (INIS)

    Fujiwara, Yoshihisa; Soda, Jiro.

    1989-08-01

    The (2+1)-dimensional Einstein gravity with a cosmological constant is studied in the ADM canonical formalism. Adopting the York's time slice, we completely solve the initial-value problem and the time evolution equations with an initial spacelike 2-surface being a closed Riemann surface of genus zero and one. The result in a torus case is that the Teichmueller parameters for the torus follow a geodesic in the Teichmueller space but its motion asymptotically stops due to the presence of the cosmological constant. (author)

  1. Open Problem: Kernel methods on manifolds and metric spaces

    DEFF Research Database (Denmark)

    Feragen, Aasa; Hauberg, Søren

    2016-01-01

    Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong...... linear properties. This negative result hints that radial kernel are perhaps not suitable over geodesic metric spaces after all. Here, however, we present evidence that large intervals of bandwidths exist where geodesic exponential kernels have high probability of being positive definite over finite...... datasets, while still having significant predictive power. From this we formulate conjectures on the probability of a positive definite kernel matrix for a finite random sample, depending on the geometry of the data space and the spread of the sample....

  2. Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory

    International Nuclear Information System (INIS)

    Soda, Jiro.

    1989-08-01

    On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)

  3. Close binary stars

    International Nuclear Information System (INIS)

    Larsson-Leander, G.

    1979-01-01

    Studies of close binary stars are being persued more vigorously than ever, with about 3000 research papers and notes pertaining to the field being published during the triennium 1976-1978. Many major advances and spectacular discoveries were made, mostly due to increased observational efficiency and precision, especially in the X-ray, radio, and ultraviolet domains. Progress reports are presented in the following areas: observational techniques, methods of analyzing light curves, observational data, physical data, structure and models of close binaries, statistical investigations, and origin and evolution of close binaries. Reports from the Coordinates Programs Committee, the Committee for Extra-Terrestrial Observations and the Working Group on RS CVn binaries are included. (Auth./C.F.)

  4. 75 FR 7370 - Closed Captioning of Video Programming; Closed Captioning Requirements for Digital Television...

    Science.gov (United States)

    2010-02-19

    ... FEDERAL COMMUNICATIONS COMMISSION 47 CFR Part 79 [CG Docket No. 05-231; ET Docket No. 99-254; FCC 08-255] Closed Captioning of Video Programming; Closed Captioning Requirements for Digital Television... Captioning of Video Programming; Closed Captioning Requirements for Digital Television Receivers, Declaratory...

  5. Shear-free axial model in massive Brans–Dicke gravity

    Energy Technology Data Exchange (ETDEWEB)

    Sharif, M., E-mail: msharif.math@pu.edu.pk [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan); Manzoor, Rubab, E-mail: rubab.manzoor@umt.edu.pk [Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590 (Pakistan); Department of Mathematics, University of Management and Technology, Johar Town Campus, Lahore-54782 (Pakistan)

    2017-01-15

    This paper explores the influences of dark energy on the shear-free axially symmetric evolution by considering self-interacting Brans–Dicke gravity as a dark energy candidate. We describe energy source of the model and derive all the effective dynamical variables as well as effective structure scalars. It is found that scalar field is one of the sources of anisotropy and dissipation. The resulting effective structure scalars help to study the dynamics associated with dark energy in any axial configuration. In order to investigate shear-free evolution, we formulate a set of governing equations along with heat transport equation. We discuss consequences of shear-free condition upon different SBD fluid models like dissipative non-geodesic and geodesic models. For dissipative non-geodesic case, the rotational distribution turns out to be the necessary and sufficient condition for radiating model. The dissipation depends upon inhomogeneous expansion. The geodesic model is found to be irrotational and non-radiating. The non-dissipative geodesic model leads to FRW model for positive values of the expansion parameter.

  6. Entropy Measures as Geometrical Tools in the Study of Cosmology

    Directory of Open Access Journals (Sweden)

    Gilbert Weinstein

    2017-12-01

    Full Text Available Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x with χ ( x being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double-warped spacetime leads to the same entropy equation. By applying a Robertson–Walker metric for a flat three-dimensional Euclidean space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Riccati equation similar to the transformed entropy equation. Those Riccati-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of general relativity and cosmology. We suggest a refined entropy measure applicable in cosmology and defined by the average deviation of the geodesics in a congruence.

  7. What's the point? Hole-ography in Poincare AdS

    International Nuclear Information System (INIS)

    Espindola, Ricardo; Gueijosa, Alberto; Landetta, Alberto; Pedraza, Juan F.

    2018-01-01

    In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS 3 via hole-ography, i.e., in terms of differential entropy of the dual CFT 2 . Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.)

  8. What's the point? Hole-ography in Poincare AdS

    Energy Technology Data Exchange (ETDEWEB)

    Espindola, Ricardo [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); University of Southampton, Mathematical Sciences and STAG Research Centre, Southampton (United Kingdom); Gueijosa, Alberto; Landetta, Alberto [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); Pedraza, Juan F. [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands)

    2018-01-15

    In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS{sub 3} via hole-ography, i.e., in terms of differential entropy of the dual CFT{sub 2}. Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.)

  9. Colliding holes in Riemann surfaces and quantum cluster algebras

    Science.gov (United States)

    Chekhov, Leonid; Mazzocco, Marta

    2018-01-01

    In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.

  10. Complete spacelike immersions with topology

    International Nuclear Information System (INIS)

    Harris, S.G.

    1988-01-01

    A fairly large class of Lorentz manifolds is defined, called WH normal manifolds, which are approximately those for which timelike infinity is a single point. It is shown that, in such a space, an immersed spacelike hypersurface which is complete must, if it is self-intersecting, not achronal or proper, satisfy strong topological conditions; in particular, if the immersion is injective in the fundamental group, then the hypersurface must be closed, embedded and achronal (i.e. a partial Cauchy surface). WH normal spaces include products of any Riemannian manifold with Minkowski 1-space; in such space, a complete immersed spacelike hypersurface must be immersed as a covering space for the Riemannian factor. (author)

  11. Born-Infeld determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Ferraro, Rafael, E-mail: ferraro@iafe.uba.a [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina); Fiorini, Franco, E-mail: franco@iafe.uba.a [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina)

    2010-08-30

    In the context of Born-Infeld determinantal gravity formulated in an n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional vacuum circular symmetric solution without cosmological constant consisting in a rotating spacetime with non-singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime.

  12. Born-Infeld determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime

    International Nuclear Information System (INIS)

    Ferraro, Rafael; Fiorini, Franco

    2010-01-01

    In the context of Born-Infeld determinantal gravity formulated in an n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional vacuum circular symmetric solution without cosmological constant consisting in a rotating spacetime with non-singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime.

  13. Recursion Formulae for Obtaining Surfaces with Constant Mean Curvature in R2,1

    International Nuclear Information System (INIS)

    Tian Yongbo; Nan Zhijie; Tian Chou

    2007-01-01

    Though the Baecklund transformation on time-like surfaces with constant mean curvature surfaces in R 2,1 has been obtained, it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the Baecklund transformation is used. For sake of this, in this article, some special work is done to reform the Baecklund transformation to a recursion formula, by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure.

  14. 27 CFR 44.146 - Closing.

    Science.gov (United States)

    2010-04-01

    ... PAYMENT OF TAX, OR WITH DRAWBACK OF TAX Operations by Export Warehouse Proprietors Inventories § 44.146 Closing. A closing inventory shall be made by the export warehouse proprietor when he transfers ownership or concludes business. Where the proprietor transfers ownership the closing inventory shall be made...

  15. 27 CFR 40.426 - Closing.

    Science.gov (United States)

    2010-04-01

    ... TOBACCO Manufacture of Cigarette Papers and Tubes Operations by Manufacturers § 40.426 Closing. A closing report, covering the period from the first of the month to the date of the closing inventory, shall be made with such inventory. (72 Stat. 1422; 26 U.S.C. 5722) Inventories ...

  16. 7 CFR 1927.56 - Scheduling loan closing.

    Science.gov (United States)

    2010-01-01

    ... REGULATIONS TITLE CLEARANCE AND LOAN CLOSING Real Estate Title Clearance and Loan Closing § 1927.56 Scheduling loan closing. The agency, in coordination with the closing agent, will arrange a loan closing and send loan closing instructions, on an agency form to the closing agent when the agency determines that the...

  17. Compatibility conditions of a singular hypersurface in the relativistic mechanics of the continuous media

    International Nuclear Information System (INIS)

    Maugin, G.A.

    1976-01-01

    In this work the compatibility conditions verified by the discontinuities of relativistic fields and of their space-time and time-like derivatives up to be second order are systematically constructed in terms of the local geometry of the wave front (singular hypersurface). A new time-like derivative that generalizes Thomas' delta-derivative of classical continuum mechanics is thus introduced in the relativistic frame. It allows to formulate these conditions in compact forms. It is thus expected that the relativistic analogue of T.Y. Thomas' (1957) classical theory is produced [fr

  18. The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets

    CERN Document Server

    Meessen, P

    2006-01-01

    We classify all the supersymmetric configurations of ungauged N=2,d=4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric configurations fall into two classes, depending on the timelike or null nature of the Killing vector constructed from Killing spinor bilinears. The timelike class configurations are essentially the ones found by Behrndt, Luest and Sabra, which exhaust this class and are the ones that include supersymmetric black holes. The null class configurations include pp-waves and cosmic strings.

  19. Kinematics of relative motion of test particles in general relativity

    International Nuclear Information System (INIS)

    Bazanski, S.L.

    1977-01-01

    A detailed mathematical study of the concept of geodesic deviation in pseudo-riemannian geometry is presented. A generalization of this concept to geodesic deviations of a higher order is then introduced and the second geodesic deviation is investigated in some detail. A geometric interpretation of the set of generalized geodesic deviations is given and applied in general relativity to determine a covariant and local description (with a desired order of accuracy) of test motions which take place in a certain finite neighbourhood of a given world line of an observer. The proper time evolution of two other objects related to geodesic deviation is also discussed: the space separation vector and the telescopic vector. This last name is given here to a field of null vectors along observer's world line which always point towards the same adjacent world line. The telescopic equations allow to determine the evolution of the frequency shift of electromagnetic radiation sent from and received on neighbouring world lines. On the basis of these equations also certain relations have been derived which connect the frequencies or frequency shifts with the curvature of space-time

  20. Sigma-model formulation of the Yang-Mills theory on four-dimensional hypersphere

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Krivonos, S.O.

    1981-01-01

    The bilocal sigma-model representation is constructed for the Yang-Mills theory in the simplest conformally flat hyperspherical spaces So(1,4)/SO(1,3), SO(2,3)/SO(1,3) and SO(5)/SO(4). Like in the case of Minkowski and Euclidean spaces, Yang-Mills potential is defined as bsub(μ)(x)=dsub(μ)sup(y)b(x,y)|y=0 , b(x,y) being a bilocal Goldstone field which takes values in the gauge group algebra and is subjected to certain covariant constraints. The minimal version of these constraints results in the ''string'' representation for b(x,y) through the P-exponential of bsub(μ)(x) along the fixed paths coinciding with geodesics. Due to the presence of closed geodesics, the contour fuctionals naturally appear in the theory, with contours being the circles with the hypersphere radius. The sigma-model representation is shown to be Weyl-covariant: its formulations indifferent conformally flat spaces are related by transformations of ysup(rho). The geometric meaning of ysup(rho) and minimal constraints is explained, and the conformal group gransformation for ysup(rho) is found [ru

  1. Sigma-model formulation of the Yang-Mills theory on four-dimensional hypersphere

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Krivonos, S.O.

    1983-01-01

    The bilocal sigma-model representation is constructed for Yang-Mills theory in the simplest conformally flat hyperspherical spases SO(1, 4)/SO(1, 3), SO(2, 3)/SO(1, 3) and SO(5)/SO(4) (for the Euclidean Yang-Mills). Like in the case of Minkowski and Euclidean spaces, Yang-Mills potential is defined as bsub(μ)(x)=dsub(μ)sup(y)b(x, y)sub(y=0), b(x, y) being a bilocal Goldstone field which takes values in the gauge group algebra and is subjected to certain covariant constraints. The minimal version of these constraints results in the ''string'' representation for b(x, y) through the P exponential of bsub(μ)(x) along the fixed paths coinciding with geodesics. Due to the presence of closed geodesics, the contour functional naturally appear in the theory, with contours being the circles with the hypersphere radius. The sigma-model representation is shown to be Weyl-covariant: its formulations in different conformally flat spaces are related by transformations of ysup(rho). The geometric meaning ysup(rho) and minimal constraints is explained, and the conformal group transofrmation of ysup(rho) is found

  2. Restaurants closed over Christmas

    CERN Multimedia

    2011-01-01

    The restaurants will be closed during the Christmas holiday period : please note that all three CERN Restaurants will be closed from 5 p.m. on Wednesday, 21 December until Wednesday, 4 January inclusive. The Restaurants will reopen on Thursday, 5 January 2012.

  3. Minding the close relationship.

    Science.gov (United States)

    Harvey, J H; Omarzu, J

    1997-01-01

    In this theoretical analysis, we argue that a process referred to as minding is essential for a couple to feel mutually close and satisfied in a close relationship over a long period Minding represents a package of mutual self-disclosure, other forms of goal-oriented behavior aimed at facilitating the relationship, and attributions about self's and other's motivations, intentions, and Mort in the relationship. Self-disclosure and attribution activities in minding are aimed at getting to know the other, trying to understand the other's motivations and deeper disposition as they pertain to the relationship, and showing respect and acceptance for knowledge gained about other. We link the concept of minding to other major ideas and literatures about how couples achieve closeness: self-disclosure and social penetration, intimacy, empathy and empathic accuracy, and love and self-expansion. We argue that the minding process articulated here has not previously been delineated and that it is a useful composite notion about essential steps in bonding among humans. We also argue that the minding concept stretches our understanding of the interface of attribution and close relationships. We present research possibilities and implications and consider possible alternative positions and counter arguments about the merits of the minding idea for close relationship satisfaction.

  4. Event and Apparent Horizon Finders for 3+1 Numerical Relativity

    Directory of Open Access Journals (Sweden)

    Thornburg Jonathan

    2007-06-01

    Full Text Available Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3+1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous null surface in spacetime. The event horizon is defined nonlocally in time: it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part of spacetime has been numerically computed.There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate.In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Theta. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most “apparent horizon” finders actually find MOTSs.There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting

  5. 7 CFR 764.402 - Loan closing.

    Science.gov (United States)

    2010-01-01

    ... SPECIAL PROGRAMS DIRECT LOAN MAKING Loan Decision and Closing § 764.402 Loan closing. (a) Signature... information for the Agency to reconfirm approval and proceed with loan closing. (3) The Agency or closing... account will be used according to subpart B of part 761 of this chapter when these processes are not...

  6. Closed string field theory

    International Nuclear Information System (INIS)

    Strominger, A.

    1987-01-01

    A gauge invariant cubic action describing bosonic closed string field theory is constructed. The gauge symmetries include local spacetime diffeomorphisms. The conventional closed string spectrum and trilinear couplings are reproduced after spontaneous symmetry breaking. The action S is constructed from the usual ''open string'' field of ghost number minus one half. It is given by the associator of the string field product which is non-vanishing because of associativity anomalies. S does not describe open string propagation because open string states associate and can thereby be shifted away. A field theory of closed and open strings can be obtained by adding to S the cubic open string action. (orig.)

  7. Cosmological horizons and reconstruction of quantum field theories

    International Nuclear Information System (INIS)

    Dappiaggi, C.; Pinamonti, N.

    2007-12-01

    As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon J - common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M - valid for de Sitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space - the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(J - ) constructed on the cosmological horizon. There is exactly one pure quasifree state λ on W(J - ) which fulfills a suitable energy positivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ induces a preferred physically meaningful quantum state λ M for the quantum theory in the bulk. If M admits a timelike Killing generator preserving J - , then the associated self-adjoint generator in the GNS representation of λ M has positive spectrum (i.e. energy). Moreover λ M turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, λ M coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for λ M in more general spacetimes are presented. (orig.)

  8. Regular black holes: electrically charged solutions, Reissner-Nordstroem outside a De Sitter core

    Energy Technology Data Exchange (ETDEWEB)

    Lemos, Jose P.S. [Universidade Tecnica de Lisboa (CENTRA/IST/UTL) (Portugal). Instituto Superior Tecnico. Centro Multidisciplinar de Astrofisica; Zanchin, Vilson T. [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil). Centro de Ciencias Naturais e Humanas

    2011-07-01

    Full text: The understanding of the inside of a black hole is of crucial importance in order to have the correct picture of a black hole as a whole. The singularities that lurk inside of the usual black hole solutions are things to avoid. Their substitution by a regular part is of great interest, the process generating regular black holes. In the present work regular black hole solutions are found within general relativity coupled to Maxwell's electromagnetism and charged matter. We show that there are objects which correspond to regular charged black holes, whose interior region is de Sitter, whose exterior region is Reissner-Nordstroem, and the boundary between both regions is made of an electrically charged spherically symmetric coat. There are several solutions: the regular nonextremal black holes with a null matter boundary, the regular nonextremal black holes with a timelike matter boundary, the regular extremal black holes with a timelike matter boundary, and the regular overcharged stars with a timelike matter boundary. The main physical and geometrical properties of such charged regular solutions are analyzed. (author)

  9. Anholonomic Cauchy problem in general relativity

    International Nuclear Information System (INIS)

    Stachel, J.

    1980-01-01

    The Lie derivative approach to the Cauchy problem in general relativity is applied to the evolution along an arbitrary timelike vector field for the case where the dynamical degrees of freedom are chosen as the (generally anholonomic) metric of the hypersurface elements orthogonal to the vector field. Generalizations of the shear, rotation, and acceleration are given for a nonunit timelike vector field, and applied to the three-plus-one breakup of the Riemann tensor into components parallel and orthogonal to the vector field, resulting in the anholonomic Gauss--Codazzi equations. A similar breakup of the Einstein field equations results in the form of the constraint and evolution equations for the anholonomic case. The results are applied to the case of a space--time with a timelike Killing vector field (stationary field) to demonstrate their utility. Other possible applications, such as in the numerical integration of the field equations, are mentioned. Definitions are given of three-index shear, rotation, and acceleration tensors, and their use in a two-plus-two decomposition of the Riemann tensor and field equations is indicated

  10. Principal Curves on Riemannian Manifolds

    DEFF Research Database (Denmark)

    Hauberg, Søren

    2015-01-01

    Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Eucl...

  11. Light escape cones in local reference frames of Kerr-de Sitter black hole spacetimes and related black hole shadows

    Science.gov (United States)

    Stuchlík, Zdeněk; Charbulák, Daniel; Schee, Jan

    2018-03-01

    We construct the light escape cones of isotropic spot sources of radiation residing in special classes of reference frames in the Kerr-de Sitter (KdS) black hole spacetimes, namely in the fundamental class of `non-geodesic' locally non-rotating reference frames (LNRFs), and two classes of `geodesic' frames, the radial geodesic frames (RGFs), both falling and escaping, and the frames related to the circular geodesic orbits (CGFs). We compare the cones constructed in a given position for the LNRFs, RGFs, and CGFs. We have shown that the photons locally counter-rotating relative to LNRFs with positive impact parameter and negative covariant energy are confined to the ergosphere region. Finally, we demonstrate that the light escaping cones govern the shadows of black holes located in front of a radiating screen, as seen by the observers in the considered frames. For shadows related to distant static observers the LNRFs are relevant.

  12. An adaptive phase space method with application to reflection traveltime tomography

    International Nuclear Information System (INIS)

    Chung, Eric; Qian, Jianliang; Uhlmann, Gunther; Zhao, Hongkai

    2011-01-01

    In this work, an adaptive strategy for the phase space method for traveltime tomography (Chung et al 2007 Inverse Problems 23 309–29) is developed. The method first uses those geodesics/rays that produce smaller mismatch with the measurements and continues on in the spirit of layer stripping without defining the layers explicitly. The adaptive approach improves stability, efficiency and accuracy. We then extend our method to reflection traveltime tomography by incorporating broken geodesics/rays for which a jump condition has to be imposed at the broken point for the geodesic flow. In particular, we show that our method can distinguish non-broken and broken geodesics in the measurement and utilize them accordingly in reflection traveltime tomography. We demonstrate that our method can recover the convex hull (with respect to the underlying metric) of unknown obstacles as well as the metric outside the convex hull. (paper)

  13. Assessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation

    Directory of Open Access Journals (Sweden)

    Mostafa Charmi

    2010-06-01

    Full Text Available Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this paper is to assess the possible substitution of the geodesic metric with the Log-Euclidean one to reduce the computational cost of a statistical surface evolution algorithm. Materials and Methods: We incorporated the Log-Euclidean metric in the statistical surface evolution algorithm framework. To achieve this goal, the statistics and gradients of diffusion tensor images were defined using the Log-Euclidean metric. Numerical implementation of the segmentation algorithm was performed in the MATLAB software using the finite difference techniques. Results: In the statistical surface evolution framework, the Log-Euclidean metric was able to discriminate the torus and helix patterns in synthesis datasets and rat spinal cords in biological phantom datasets from the background better than the Euclidean and J-divergence metrics. In addition, similar results were obtained with the geodesic metric. However, the main advantage of the Log-Euclidean metric over the geodesic metric was the dramatic reduction of computational cost of the segmentation algorithm, at least by 70 times. Discussion and Conclusion: The qualitative and quantitative results have shown that the Log-Euclidean metric is a good substitute for the geodesic metric when using a statistical surface evolution algorithm in DTIs segmentation.

  14. From big bang to big crunch and beyond

    International Nuclear Information System (INIS)

    Elitzur, Shmuel; Rabinovici, Eliezer; Giveon, Amit; Kutasov, David

    2002-01-01

    We study a quotient Conformal Field Theory, which describes a 3+1 dimensional cosmological spacetime. Part of this spacetime is the Nappi-Witten (NW) universe, which starts at a 'big bang' singularity, expands and then contracts to a 'big crunch' singularity at a finite time. The gauged WZW model contains a number of copies of the NW spacetime, with each copy connected to the preceding one and to the next one at the respective big bang/big crunch singularities. The sequence of NW spacetimes is further connected at the singularities to a series of non-compact static regions with closed timelike curves. These regions contain boundaries, on which the observables of the theory live. This suggests a holographic interpretation of the physics. (author)

  15. Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms

    International Nuclear Information System (INIS)

    Lawn, Marie-Amélie; Roth, Julien

    2011-01-01

    We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. This generalizes a recent work of the first author for spacelike immersed Lorentzian surfaces in ℝ 2,1 to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0, 2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.

  16. ON NANO Λg-CLOSED SETS

    OpenAIRE

    Rajasekaran, Ilangovan; Nethaji, Ochanan

    2017-01-01

    Abstaract−In this paper, we introduce nano ∧g-closed sets in nano topological spaces. Some properties of nano ∧g-closed sets and nano ∧g-open sets are weaker forms of nano closed sets and nano open sets

  17. A Random Riemannian Metric for Probabilistic Shortest-Path Tractography

    DEFF Research Database (Denmark)

    Hauberg, Søren; Schober, Michael; Liptrot, Matthew George

    2015-01-01

    of the diffusion tensor as a “random Riemannian metric”, where a geodesic is a distribution over tracts. We approximate this distribution with a Gaussian process and present a probabilistic numerics algorithm for computing the geodesic distribution. We demonstrate SPT improvements on data from the Human Connectome...

  18. Cut Locus Construction using Deformable Simplicial Complexes

    DEFF Research Database (Denmark)

    Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas; Anton, François

    2011-01-01

    In this paper we present a method for appproximating cut loci for a given point p on Riemannian 2D manifolds, closely related to the notion of Voronoi diagrams. Our method finds the cut locus by advecting a front of points equally distant from p along the geodesics originating at p and finding...... the domain to have disk topology. We test our method for tori of revolution and compare our results to the benchmark ones from [2]. The method, however, is generic and can be easily adapted to construct cut loci for other manifolds of genera other than 1....

  19. Oriented open-closed string theory revisited

    International Nuclear Information System (INIS)

    Zwiebach, B.

    1998-01-01

    String theory on D-brane backgrounds is open-closed string theory. Given the relevance of this fact, we give details and elaborate upon our earlier construction of oriented open-closed string field theory. In order to incorporate explicitly closed strings, the classical sector of this theory is open strings with a homotopy associative A ∞ algebraic structure. We build a suitable Batalin-Vilkovisky algebra on moduli spaces of bordered Ricmann surfaces, the construction of which involves a few subtleties arising from the open string punctures and cyclicity conditions. All vertices coupling open and closed strings through disks are described explicitly. Subalgebras of the algebra of surfaces with boundaries are used to discuss symmetries of classical open string theory induced by the closed string sector, and to write classical open string field theory on general closed string backgrounds. We give a preliminary analysis of the ghost-dilaton theorem. copyright 1998 Academic Press, Inc

  20. Some studies on arithmetical chaos in classical and quantum mechanics

    International Nuclear Information System (INIS)

    Bolte, J.

    1993-04-01

    Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)

  1. Closed recirculation-Water treatment

    International Nuclear Information System (INIS)

    Hamza, Hamza B.; Ben Ali, Salah; Saad, Mohamed A.; Traish, Massud R.

    2005-01-01

    This water treatment is a practical work applied in the center, for a closed recirculation-water system. The system had experienced a serious corrosion problem, due to the use of inadequate water. This work includes chemical preparation for the system. Water treatment, special additives, and follow-up, which resulted in the stability of the case. This work can be applied specially for closed recirculation warm, normal, and chilled water. (author)

  2. High current vacuum closing switch

    International Nuclear Information System (INIS)

    Dolgachev, G.I.; Maslennikov, D.D.; Romanov, A.S.; Ushakov, A.G.

    2005-01-01

    The paper proposes a powerful pulsed closing vacuum switch for high current commutation consisting of series of the vacuum diodes with near 1 mm gaps having closing time determined by the gaps shortening with the near-electrode plasmas [ru

  3. A virtual closed loop method for closed loop identification

    NARCIS (Netherlands)

    Agüero, J.C.; Goodwin, G.C.; Hof, Van den P.M.J.

    2011-01-01

    Indirect methods for the identification of linear plant models on the basis of closed loop data are based on the use of (reconstructed) input signals that are uncorrelated with the noise. This generally requires exact (linear) controller knowledge. On the other hand, direct identification requires

  4. 7 CFR 1927.58 - Closing the transaction.

    Science.gov (United States)

    2010-01-01

    ... REGULATIONS TITLE CLEARANCE AND LOAN CLOSING Real Estate Title Clearance and Loan Closing § 1927.58 Closing the transaction. The closing agent will cooperate with the approval official, borrower, seller, and... when a loan is being made to a borrower who already owns the real estate to be mortgaged. This...

  5. On some properties of conjugacy closed loops

    International Nuclear Information System (INIS)

    Adeniran, John Olusola

    2002-07-01

    It is shown that central loops are not conjugacy closed loops but instead are loops of units in their loop algebras that are conjugacy closed. It is also shown that certain inner mappings of a conjugacy closed loop are nuclear. Some invariants of left conjugacy closed loops are obtained. (author)

  6. High energy particle collisions near black holes

    Directory of Open Access Journals (Sweden)

    Zaslavskii O. B.

    2016-01-01

    Full Text Available If two geodesic particles collide near a rotating black hole, their energy in the centre of mass frame Ec.m. can become unbound under certain conditions (the so-called BSW effect. The special role is played here by so-called critical geodesics when one of particles has fine-tuned energy and angular momentum. The nature of geodesics reveals itself also in fate of the debris after collisions. One of particles moving to a remote observer is necessarily near-critical. We discuss, when such a collision can give rise not only unboud Ec.m. but also unbound Killing energy E (so-called super-Penrose process.

  7. The real meaning of complex Minkowski-space world-lines

    Energy Technology Data Exchange (ETDEWEB)

    Adamo, T M [University of Oxford, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB (United Kingdom); Newman, E T, E-mail: newman@pitt.ed [University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, PA 15213 (United States)

    2010-04-07

    In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.

  8. The real meaning of complex Minkowski-space world-lines

    International Nuclear Information System (INIS)

    Adamo, T M; Newman, E T

    2010-01-01

    In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.

  9. Estimates of the first Dirichlet eigenvalue from exit time moment spectra

    DEFF Research Database (Denmark)

    Hurtado, Ana; Markvorsen, Steen; Palmer, Vicente

    2013-01-01

    We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball...

  10. The effect of sources on horizons that may develop when plane gravitational waves collide

    International Nuclear Information System (INIS)

    Chandrasekhar, Subrahmanyan; Xanthopoulos, B.C.

    1987-01-01

    Colliding plane gravitational waves that lead to the development of a horizon and a subsequent time-like singularity are coupled with an electromagnetic field, a perfect fluid, and null dust (consisting of massless particles). The coupling of the gravitational waves with an electromagnetic field does not affect, in any essential way, the development of the horizon or the time-like singularity if the polarizations of the colliding gravitational waves are not parallel. If the polarizations are parallel, the space-like singularity which occurs in the vacuum is transformed into a horizon followed by a three-dimensional time-like singularity by the merest presence of the electromagnetic field. The coupling of the gravitational waves with a perfect fluid and null dust affect the development of horizons and singularities in radically different ways: the perfect fluid affects the development decisively in all cases but qualitatively in the same way, while null dust prevents the development of horizons and allows only the development of space-like singularities. The contrasting behaviours of a perfect fluid and of null dust in the framework of general relativity is compared with the behaviours one may expect, under similar circumstances, in the framework of special relativity. (author)

  11. Search for open-quote open-quote polarized close-quote close-quote instantons in the vacuum

    International Nuclear Information System (INIS)

    Kuchiev, M.Y.

    1996-01-01

    The new phase of a gauge theory in which the instantons are open-quote open-quote polarized,close-quote close-quote i.e., have the preferred orientation, is discussed. A class of gauge theories with the specific condensates of the scalar fields is considered. In these models there exists an interaction between instantons resulting from one-fermion loop corrections. The interaction makes the identical orientation of instantons the most probable, permitting one to expect the system to undergo a phase transition into the state with polarized instantons. The existence of this phase is confirmed in the mean-field approximation in which there is a first-order phase transition separating the open-quote open-quote polarized phase close-quote close-quote from the usual nonpolarized one. The considered phase can be important for the description of gravity in the framework of the gauge field theory. copyright 1996 The American Physical Society

  12. Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae

    International Nuclear Information System (INIS)

    Bleher, P.M.; Kosygin, D.V.; Sinai, Y.G.

    1995-01-01

    We consider the Weyl asymptotic formula [{E n ≤R 2 }=Area Q.R 2 /(4π)+n(R), for eigenvalues of the Laplace-Beltrami operator on a two-dimensional torus Q with a Liouville metric which is in a sense the most general case of an integrable metric. We prove that if the surface Q is non-degenerate then the remainder term n(R) has the form n(R)=R 1/2 θ(R), where θ(R) is an almost periodic function of the Besicovitch class B 1 , and the Fourier amplitudes and the Fourier frequencies of θ(R) can be expressed via lengths of closed geodesics on Q and other simple geometric characteristics of these geodesics. We prove then that if the surface Q is generic then the limit distribution of θ(R) has a density p(t), which is an entire function of t possessing an asymptotics on a real line, logp(t)∝-C ± t 4 as t→±∞. An explicit expression for the Fourier transform of p(t) via Fourier amplitudes of θ(R) is also given. We obtain the analogue of the Guillemin-Duistermaat trace formula for the Liouville surfaces and discuss its accuracy. (orig.)

  13. IIB backgrounds with five-form flux

    International Nuclear Information System (INIS)

    Gran, U.; Gutowski, J.; Papadopoulos, G.

    2008-01-01

    We investigate all N=2 supersymmetric IIB supergravity backgrounds with non-vanishing five-form flux. The Killing spinors have stability subgroups Spin(7) x R 8 , SU(4) x R 8 and G 2 . In the SU(4) x R 8 case, two different types of geometry arise depending on whether the Killing spinors are generic or pure. In both cases, the backgrounds admit a null Killing vector field which leaves invariant the SU(4) x R 8 structure, and an almost complex structure in the directions transverse to the lightcone. In the generic case, the twist of the vector field is trivial but the almost complex structure is non-integrable, while in the pure case the twist is non-trivial but the almost complex structure is integrable and associated with a relatively balanced Hermitian structure. The G 2 backgrounds admit a time-like Killing vector field and two spacelike closed one-forms, and the seven directions transverse to these admit a co-symplectic G 2 structure. The Spin(7) x R 8 backgrounds are pp-waves propagating in an eight-dimensional manifold with holonomy Spin(7). In addition we show that all the supersymmetric solutions of simple five-dimensional supergravity with a time-like Killing vector field, which include the AdS 5 black holes, lift to SU(4) x R 8 pure Killing spinor IIB backgrounds. We also show that the LLM solution is associated with a co-symplectic co-homogeneity one G 2 manifold which has principal orbit S 3 xS 3

  14. Bell's inequalities from the field concept in general relativity

    International Nuclear Information System (INIS)

    Sachs, M.

    1980-01-01

    A nonlinear field theory of matter, based axiomatically on general relativity, has an asymptotic, low-energy limit that predicts the outcome of experimental tests of Bell's inequalities. The inequalities should follow if spin-correlated, spin-1/2 particles, observed in coincidence, were a spacelike distance apart; they should be violated if they were separated by timelike distances. The experiment at timelike separations, for scattered protons observed in coincidence, was carried out by Lahemi-Rachti and Mittig and, thus far, agrees with this theory. Extension of the low-energy pp scattering experiment to observations at spacelike distances is suggested, with the prediction that agreement should be obtained with Bell's inequalities there. (author)

  15. Scaling violations beyond the leading order

    CERN Document Server

    Petronzio, R

    1981-01-01

    The authors are concerned with the explicit construction of a method which generalizes beyond leading order the simple probabilistic interpretation of leading scaling violations. The results obtained in this language allow to predict the evolution with the variation of external invariants not only of 'space-like' processes, where the off- shell partons starting the hard interaction have space-like four momenta, like in the case of deep inelastic scattering or Drell-Yan, but also of 'time-like' processes, like the one-particle inclusive e /sup +/e/sup -/ annihilation, where the partons acting in the fragmentation functions have 'time-like' off-shell invariant masses. (9 refs).

  16. Gravitational collapse disturbs the dS/CFT correspondence?

    International Nuclear Information System (INIS)

    Iwashita, Yukinori; Yoshino, Hirotaka; Shiromizu, Tetsuya

    2005-01-01

    We study the gravitational collapse in five-dimensional de Sitter (dS) spacetime and discuss the existence of the conformal boundaries at future timelike infinity (I + ) from the perspective of the dS/conformal field theories correspondence. We investigate the motion of a spherical dust shell and the black-hole area bounds. The latter includes the analysis of the trapping horizon and the initial data with spindle-shaped matter distribution. In all the above analyses we find the evidences that guarantee the existence of the conformal boundaries at future timelike infinity which may be essential to apply the dS/conformal field theories correspondence

  17. The momentum degree of freedom of elementary particles and the gravitation

    International Nuclear Information System (INIS)

    Tati, Takao.

    1978-01-01

    A universal time-like vector has been introduced into the momentum space of elementary particles, in a quantum field theory with a finite degree of freedom, in order to specify the Lorentz-system in which the cutoff function of momentum is given. In this paper, the relationship between quantum field theory and general relativity is considered and it is argued that, when the effect of gravitation on the momentum degree of freedom is taken into account, the universal time-like vector depends on the position of macroscopic space-time and can be considered, in a cosmological model, to coincide, on an average, with the Weyl's cosmic time. (auth.)

  18. Violation of causality in f(T) gravity

    Energy Technology Data Exchange (ETDEWEB)

    Otalora, G. [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Reboucas, M.J. [Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ (Brazil)

    2017-11-15

    In the standard formulation, the f(T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f(T) gravity. A locally Lorentz covariant f(T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f(T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Goedel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f(T) theories, we examine whether they admit Goedel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Goedel-type solution, which contains special solutions in which the essential parameter of Goedel-type geometries, m{sup 2}, defines any class of homogeneous Goedel-type geometries. We show that solutions of the trigonometric and linear classes (m{sup 2} < 0 and m = 0) are permitted only for the combined matter sources with an electromagnetic field matter component. We extended to the context of covariant f(T) gravity a theorem which ensures that any perfect-fluid homogeneous Goedel-type solution defines the same set of Goedel tetrads h{sub A}{sup μ} up to a Lorentz transformation. We also showed that the single massless scalar field generates Goedel-type solution with no closed time-like curves. Even though the covariant f(T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Goedel-type solutions makes apparent that the covariant formulation of f(T) gravity

  19. Close-In Substellar Companions and the Formation of sdB-Type Close Binary Stars

    Directory of Open Access Journals (Sweden)

    L. Y. Zhu

    2015-02-01

    Full Text Available The sdB-type close binaries are believed to have experienced a common-envelope phase and may evolve into cataclysmic binaries (CVs. About 10% of all known sdB binaries are eclipsing binaries consisting of very hot subdwarf primaries and low-mass companions with short orbital periods. The eclipse profiles of these systems are very narrow and deep, which benefits the determination of high precise eclipsing times and makes the detection of small and close-in tertiary bodies possible. Since 2006 we have monitored some sdB-type eclipsing binaries to search for the close-in substellar companions by analyzing the light travel time effect. Here some progresses of the program are reviewed and the formation of sdB-type binary is discussed.

  20. Observing the Progressive Decoherence of the open-quote open-quote Meter close-quote close-quote in a Quantum Measurement

    International Nuclear Information System (INIS)

    Brune, M.; Hagley, E.; Dreyer, J.; Maitre, X.; Maali, A.; Wunderlich, C.; Raimond, J.M.; Haroche, S.

    1996-01-01

    A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time with a few photon coherent fields trapped in a high Q microwave cavity. The mesoscopic superposition was the equivalent of an open-quote open-quote atom+measuringapparatus close-quote close-quote system in which the open-quote open-quote meter close-quote close-quote was pointing simultaneously towards two different directions emdash a open-quote open-quote Schroedinger cat.close-quote close-quote The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement. copyright 1996 The American Physical Society

  1. Open-closed homotopy algebra in mathematical physics

    International Nuclear Information System (INIS)

    Kajiura, Hiroshige; Stasheff, Jim

    2006-01-01

    In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A ∞ algebras) by closed strings (L ∞ algebras)

  2. Geodetic achievement and avoidance games for graphs | Haynes ...

    African Journals Online (AJOL)

    Let G = (V,E) be a nontrivial connected graph. For a subset S ⊆ V, the geodesic closure (S) of S is the set of all vertices on geodesics (shortest paths) between two vertices of S. We study the geodetic achievement and avoidance games defined by Buckley and Harary (Geodetic games for graphs, Quaestiones Math.

  3. Diffusion of massive particles around an Abelian-Higgs string

    Science.gov (United States)

    Saha, Abhisek; Sanyal, Soma

    2018-03-01

    We study the diffusion of massive particles in the space time of an Abelian Higgs string. The particles in the early universe plasma execute Brownian motion. This motion of the particles is modeled as a two dimensional random walk in the plane of the Abelian Higgs string. The particles move randomly in the space time of the string according to their geodesic equations. We observe that for certain values of their energy and angular momentum, an overdensity of particles is observed close to the string. We find that the string parameters determine the distribution of the particles. We make an estimate of the density fluctuation generated around the string as a function of the deficit angle. Though the thickness of the string is small, the length is large and the overdensity close to the string may have cosmological consequences in the early universe.

  4. On the equivalence of inertial and gravitational mass of extended bodies in metric theories of gravity

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Chugreev, Yu.V.

    1985-01-01

    It is shown that in any metric theory of gravitation passessing conservation laws for energy-momentum of the substance and gravitational field taken together, the motion of centre of extended body mass occurs not according to the geodesic Riemann space-time. The centre of mass of the extended body during its motion about the orbit makes a vibrational movement in relation to supporting geodesic. Application of obtained general formulas to the Sun-Earth system and the use of experimental results on the Moon location with the regard of other experiments has shown with high accuracy of 10 -10 that the relation of gravitational passive Earth mass to its inert mass does not equal to 1 differing from it about 10 -8 . The Earth at its orbital motion makes a vibrational movement in relation to supporting geodesic with a period of 1 hour and amplitude not less than 10 -2 sm. the deviation of the Earth mass center motion from geodesic movement can be found in a corresponding experiment having a postnewton accuracy degree

  5. Thermodynamics and Hawking radiation of five-dimensional rotating charged Goedel black holes

    International Nuclear Information System (INIS)

    Wu Shuangqing; Peng Junjin

    2011-01-01

    We study the thermodynamics of Goedel-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed timelike curves and the absence of a globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, we extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and the effective action give the same Hawking fluxes as those from the Planck distribution for blackbody radiation in the background of the charged rotating Goedel black holes. Our results further support that Hawking radiation is a quantum phenomenon arising at the event horizon.

  6. Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Everett, Allen

    2004-01-01

    We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves. In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events become certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the 'many worlds interpretation'. We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments

  7. Parity horizons in shape dynamics

    International Nuclear Information System (INIS)

    Herczeg, Gabriel

    2016-01-01

    I introduce the notion of a parity horizon, and show that many simple solutions of shape dynamics possess them. I show that the event horizons of the known asymptotically flat black hole solutions of shape dynamics are parity horizons and that this notion of parity implies that these horizons possess a notion of CPT invariance that can in some cases be extended to the solution as a whole. I present three new solutions of shape dynamics with parity horizons and find that not only do event horizons become parity horizons in shape dynamics, but observer-dependent horizons and Cauchy horizons do as well. The fact that Cauchy horizons become (singular) parity horizons suggests a general chronology protection mechanism in shape dynamics that prevents the formation of closed timelike curves. (paper)

  8. Generalized threshold resummation for semi-inclusive e+e- annihilation

    International Nuclear Information System (INIS)

    Lo Presti, N.A.; Vogt, A.

    2012-02-01

    Recently methods have been developed to extend the resummation of large-x double logarithms in inclusive deep-inelastic scattering (DIS) to terms not addressed by the soft-gluon exponentiation. Here we briefly outline our approach based on fixed-order results, the general large-x structure in dimensional regularization and the all-order factorization of mass singularities, which is directly applicable also to semi-inclusive e + e - annihilation (SIA). We then present some main results for the corresponding timelike splitting functions and transverse and longitudinal fragmentation functions. The close relation between DIS and SIA facilitates the determination of additional third-order results for the latter function which is fully known only at the next-to-leading order. Therefore all above quantities can be resummed at next-to-next-to-leading logarithmic accuracy. (orig.)

  9. Test fields on compact spacetimes: Problems, some partial results and speculations

    International Nuclear Information System (INIS)

    Yurtsever, U.

    1989-09-01

    In this paper we study some basic aspects of (Lorentzian) field theory on compact Lorentz manifolds. All compact spacetimes are acausal, i.e. possess closed timelike curves; this makes them a useful testbed in analyzing some new notions of causality that we will introduce for more general acausal spacetimes. In addition, studying compact spacetimes in their own right raises a wide range of fascinating mathematical problems some of which we will explore. We will see that it is reasonable to expect Lorentzian field theory on a compact spacetime to provide information on the topology of the underlying manifold; if this is true, then this information is likely to be ''orthogonal'' (or complementary) to the information obtained through the study of Euclidean field theory. (author). 45 refs, 2 figs

  10. On the n-body problem on surfaces of revolution

    Science.gov (United States)

    Stoica, Cristina

    2018-05-01

    We explore the n-body problem, n ≥ 3, on a surface of revolution with a general interaction depending on the pairwise geodesic distance. Using the geometric methods of classical mechanics we determine a large set of properties. In particular, we show that Saari's conjecture fails on surfaces of revolution admitting a geodesic circle. We define homographic motions and, using the discrete symmetries, prove that when the masses are equal, they form an invariant manifold. On this manifold the dynamics are reducible to a one-degree of freedom system. We also find that for attractive interactions, regular n-gon shaped relative equilibria with trajectories located on geodesic circles typically experience a pitchfork bifurcation. Some applications are included.

  11. Hosotani model in closed string theory

    International Nuclear Information System (INIS)

    Shiraishi, Kiyoshi.

    1988-11-01

    Hosotani mechanism in the closed string theory with current algebra symmetry is described by the (old covariant) operator method. We compare the gauge symmetry breaking mechanism in a string theory which has SU(2) symmetry with the one in an equivalent compactified closed string theory. We also investigate the difference between Hosotani mechanism and Higgs mechanism in closed string theories by calculation of a fourpoint amplitude of 'Higgs' bosons at tree level. (author)

  12. Anisotropic, nonsingular early universe model leading to a realistic cosmology

    International Nuclear Information System (INIS)

    Dechant, Pierre-Philippe; Lasenby, Anthony N.; Hobson, Michael P.

    2009-01-01

    We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular 'pancaking' solution: the hypersurface volume goes to zero instantaneously at the 'big bang', but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the big bang. We demonstrate that there exist geodesics extending through the big bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the big bang, rendering it, at worst, a quasiregular singularity. The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasiregular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropization and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [T. S. Pereira, C. Pitrou, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 9 (2007) 6.][C. Pitrou, T. S. Pereira, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 4 (2008) 4.][A. Guemruekcueoglu, C. Contaldi, and M. Peloso, J. Cosmol. Astropart. Phys. 11 (2007) 005.]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalizes the known bouncing solution in closed FRW universes.

  13. Closing the loop.

    Science.gov (United States)

    Dassau, E; Atlas, E; Phillip, M

    2010-02-01

    The dream of closing the loop is actually the dream of creating an artificial pancreas and freeing the patients from being involved with the care of their own diabetes. Insulin-dependent diabetes (type 1) is a chronic incurable disease which requires constant therapy without the possibility of any 'holidays' or insulin-free days. It means that patients have to inject insulin every day of their life, several times per day, and in order to do it safely they also have to measure their blood glucose levels several times per day. Patients need to plan their meals, their physical activities and their insulin regime - there is only very small room for spontaneous activities. This is why the desire for an artificial pancreas is so strong despite the fact that it will not cure the diabetic patients. Attempts to develop a closed-loop system started in the 1960s but never got to a clinical practical stage of development. In recent years the availability of continuous glucose sensors revived those efforts and stimulated the clinician and researchers to believe that closing the loop might be possible nowadays. Many papers have been published over the years describing several different ideas on how to close the loop. Most of the suggested systems have a sensing arm that measures the blood glucose repeatedly or continuously, an insulin delivery arm that injects insulin upon command and a computer that makes the decisions of when and how much insulin to deliver. The differences between the various published systems in the literature are mainly in their control algorithms. However, there are also differences related to the method and site of glucose measurement and insulin delivery. SC glucose measurements and insulin delivery are the most studied option but other combinations of insulin measurements and glucose delivery including intravascular and intraperitoneal (IP) are explored. We tried to select recent publications that we believe had influenced and inspired people interested

  14. 27 CFR 70.485 - Closing agreements.

    Science.gov (United States)

    2010-04-01

    ... Relating to Alcohol, Tobacco, Firearms, and Explosives Administrative Remedies § 70.485 Closing agreements... disadvantage through consummation of such an agreement. (b) Scope of closing agreement—(1) In general. A...

  15. a geometric property of the sierpiński carpet

    African Journals Online (AJOL)

    The main aim of this paper is to find formulae for the computation of the geodesic metric on the Sierpiński carpet. This is accomplished by introducing carpet coordinates. Subsequently we show the equivalence of the Euclidean and the geodesic metric on this fractal. Mathematics Subject Classification (2000): 28A80, 54E35 ...

  16. Chaos in Kundt Type-III Spacetimes

    International Nuclear Information System (INIS)

    Sakalli, I.; Halilsoy, M.

    2011-01-01

    We consider geodesic motion in a particular Kundt type-III spacetime in which the Einstein-Yang-Mills equations admit the solutions. On a particular surface as constraint, we project the geodesics into the (x, y) plane and treat the problem as a two-dimensional one. Our numerical study shows that chaotic behavior emerges under reasonable conditions. (general)

  17. Inflation in a closed universe

    Science.gov (United States)

    Ratra, Bharat

    2017-11-01

    To derive a power spectrum for energy density inhomogeneities in a closed universe, we study a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and nonrelativistic matter epochs. (For our purposes it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invariant quantum-mechanical initial conditions in the Lorentzian section of the inflating closed de Sitter space derived from Hawking's prescription that the quantum state of the universe only include field configurations that are regular on the Euclidean (de Sitter) sphere section. The constants of integration in the radiation and matter epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. The matter epoch power spectrum of gauge-invariant energy density inhomogeneities is not a power law, and depends on spatial wave number in the way expected for a generalization to the closed model of the standard flat-space scale-invariant power spectrum. The power spectrum we derive appears to differ from a number of other closed inflation model power spectra derived assuming different (presumably non de Sitter invariant) initial conditions.

  18. Cosmological horizons and reconstruction of quantum field theories

    Energy Technology Data Exchange (ETDEWEB)

    Dappiaggi, C.; Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Trento Univ., Povo (Italy). Istituto Nazionale di Alta Matematica ' ' F. Severi' ' - GNFM; Moretti, V. [Trento Univ. (Italy). Dipt. di Matematica]|[Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Trento, Povo (Italy)

    2007-12-15

    As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon J{sup -} common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M - valid for de Sitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space - the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(J{sup -}) constructed on the cosmological horizon. There is exactly one pure quasifree state {lambda} on W(J{sup -}) which fulfills a suitable energy positivity condition with respect to a generator related with the cosmological time displacements. Furthermore {lambda} induces a preferred physically meaningful quantum state {lambda}{sub M} for the quantum theory in the bulk. If M admits a timelike Killing generator preserving J{sup -}, then the associated self-adjoint generator in the GNS representation of {lambda}{sub M} has positive spectrum (i.e. energy). Moreover {lambda}{sub M} turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, {lambda}{sub M} coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for {lambda}{sub M} in more general spacetimes are presented. (orig.)

  19. A and B Theories of Closed Time

    Directory of Open Access Journals (Sweden)

    Phill Dowe

    Full Text Available ABSTRACT Closed time is possible in several senses of ‘possible’. One might like to know, therefore, whether closed time is possible in the sense that it is compatible with standard metaphysical theories of time. In this paper I am concerned with whether closed time is compatible with A and/or B theories of time. A common enough view amongst philosophers is that B theories do but A theories do not allow closed time. However, I show that prima-facie neither approach allows closed time, but that with a little work standard versions of both approaches do. This shows that there’s no special problem with the notion of eternal return.

  20. 76 FR 76449 - Post Office Closing

    Science.gov (United States)

    2011-12-07

    ... the closing of the Spring Dale, West Virginia post office has been filed. It identifies preliminary... Postal Service's determination to close the Spring Dale post office in Spring Dale, West Virginia. The...

  1. Design Principles for Closed Loop Supply Chains

    NARCIS (Netherlands)

    H.R. Krikke (Harold); C.P. Pappis (Costas); G.T. Tsoulfas; J.M. Bloemhof-Ruwaard (Jacqueline)

    2001-01-01

    textabstractIn this paper we study design principles for closed loop supply chains. Closed loop supply chains aim at closing material flows thereby limiting emission and residual waste, but also providing customer service at low cost. We study 'traditional' and 'new' design principles known in the

  2. On the time arrows, and randomness in cosmological signals

    Directory of Open Access Journals (Sweden)

    Gurzadyan V.G.

    2013-09-01

    Full Text Available Arrows of time - thermodynamical, cosmological, electromagnetic, quantum mechanical, psychological - are basic properties of Nature. For a quantum system-bath closed system the de-correlated initial conditions and no-memory (Markovian dynamics are outlined as necessary conditions for the appearance of the thermodynamical arrow. The emergence of the arrow for the system evolving according to non-unitary dynamics due to the presence of the bath, then, is a result of limited observability, and we conjecture the arrow in the observable Universe as determined by the dark sector acting as a bath. The voids in the large scale matter distribution induce hyperbolicity of the null geodesics, with possible observational consequences.

  3. On the time arrows, and randomness in cosmological signals

    Science.gov (United States)

    Gurzadyan, V. G.; Sargsyan, S.; Yegorian, G.

    2013-09-01

    Arrows of time - thermodynamical, cosmological, electromagnetic, quantum mechanical, psychological - are basic properties of Nature. For a quantum system-bath closed system the de-correlated initial conditions and no-memory (Markovian) dynamics are outlined as necessary conditions for the appearance of the thermodynamical arrow. The emergence of the arrow for the system evolving according to non-unitary dynamics due to the presence of the bath, then, is a result of limited observability, and we conjecture the arrow in the observable Universe as determined by the dark sector acting as a bath. The voids in the large scale matter distribution induce hyperbolicity of the null geodesics, with possible observational consequences.

  4. On integrable c < 1 open-closed string theory

    International Nuclear Information System (INIS)

    Johnson, C.V.

    1994-01-01

    The integrable structure of open-closed string theories in the (p, q) conformal minimal model backgrounds is presented. The relation between the τ-function of the closed string theory and that of the open-closed string theory is uncovered. The resulting description of the open-closed string theory is shown to fit very naturally into the framework of the sl(q, C) KdV hierarchies. In particular, the twisted bosons which underlie and organise the structure of the closed string theory play a similar role here and may be employed to derive loop equations and correlation function recursion relations for the open-closed strings in a simple way. (orig.)

  5. 7 CFR 1927.54 - Requirements for closing agents.

    Science.gov (United States)

    2010-01-01

    ... closing agent and close agency real estate loans, provide necessary title clearance, and perform such... PROGRAM REGULATIONS TITLE CLEARANCE AND LOAN CLOSING Real Estate Title Clearance and Loan Closing § 1927... practice law in the state where the real estate security is located and who complies with the bonding and...

  6. 40 CFR 73.38 - Closing of accounts.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 16 2010-07-01 2010-07-01 false Closing of accounts. 73.38 Section 73...) SULFUR DIOXIDE ALLOWANCE SYSTEM Allowance Tracking System § 73.38 Closing of accounts. (a) General... close the general account by submitting an allowance transfer, pursuant to § 73.50 and § 73.52...

  7. Supersymmetric solutions of N =(1 ,1 ) general massive supergravity

    Science.gov (United States)

    Deger, N. S.; Nazari, Z.; Sarıoǧlu, Ö.

    2018-05-01

    We construct supersymmetric solutions of three-dimensional N =(1 ,1 ) general massive supergravity (GMG). Solutions with a null Killing vector are, in general, pp-waves. We identify those that appear at critical points of the model, some of which do not exist in N =(1 ,1 ) new massive supergravity (NMG). In the timelike case, we find that many solutions are common with NMG, but there is a new class that is genuine to GMG, two members of which are stationary Lifshitz and timelike squashed AdS spacetimes. We also show that in addition to the fully supersymmetric AdS vacuum, there is a second AdS background with a nonzero vector field that preserves 1 /4 supersymmetry.

  8. Negative-mass lagging cores of the big bang

    International Nuclear Information System (INIS)

    Miller, B.D.

    1976-01-01

    Examples are given of spherically symmetric cosmological models containing space-sections with the following properties: at large values of the geometrically defined coordinate R, the mass is positive, while at small values of R, the mass is negative. The negative-mass region of spacetime has local properties similar to those of the negative-mass Schwarzschild solution. The big bang in these models is partially spacelike and partially timelike, so the spacetimes do not obey the strong form of the cosmic censorship hypothesis. The timelike, negative-mass segments of the big bang are unlimited sources of electromagnetic and gravitational radiation, and as such may be attractive as ''lagging core'' models of highly energetic astrophysical phenomena

  9. Negative-mass lagging cores of the big bang

    Energy Technology Data Exchange (ETDEWEB)

    Miller, B.D.

    1976-09-01

    Examples are given of spherically symmetric cosmological models containing space-sections with the following properties: at large values of the geometrically defined coordinate R, the mass is positive, while at small values of R, the mass is negative. The negative-mass region of spacetime has local properties similar to those of the negative-mass Schwarzschild solution. The big bang in these models is partially spacelike and partially timelike, so the spacetimes do not obey the strong form of the cosmic censorship hypothesis. The timelike, negative-mass segments of the big bang are unlimited sources of electromagnetic and gravitational radiation, and as such may be attractive as ''lagging core'' models of highly energetic astrophysical phenomena. (AIP)

  10. On electric field in anti-de Sitter spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Cheong, Lee Yen, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Yan, Chew Xiao, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Ching, Dennis Ling Chuan, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my [Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Bandar Seri Iskandar, Tronoh 31750, Perak (Malaysia)

    2014-10-24

    In this paper we calculate the electromagnetic field produced using retarded Green's function in Anti-de Sitter spacetime (AdS). Since this spacetime is non-globally hyperbolic and has no Cauchy surface, we only consider the field originated from a charge moving along its geodesic in the region consists of points covered by future null geodesic of the charge.

  11. Molecular-state close-coupling theory including continuum states. I. Derivation of close-coupled equations

    International Nuclear Information System (INIS)

    Thorson, W.R.; Bandarage, G.

    1988-01-01

    We formulate a close-coupling theory of slow ion-atom collisions based on molecular (adiabatic) electronic states, and including the electronic continuum. The continuum is represented by packet states spanning it locally and constructed explicitly from exact continuum states. Particular attention is given to two fundamental questions: (1) Unbound electrons can escape from the local region spanned by the packet states. We derive close-coupled integral equations correctly including the escape effects; the ''propagator'' generated by these integral equations does not conserve probability within the close-coupled basis. Previous molecular-state formulations including the continuum give no account of escape effects. (2) Nonadiabatic couplings of adiabatic continuum states with the same energy are singular, reflecting the fact that an adiabatic description of continuum behavior is not valid outside a local region. We treat these singularities explicitly and show that an accurate representation of nonadiabatic couplings within the local region spanned by a set of packet states is well behaved. Hence an adiabatic basis-set description can be used to describe close coupling to the continuum in a local ''interaction region,'' provided the effects of escape are included. In principle, the formulation developed here can be extended to a large class of model problems involving many-electron systems and including models for Penning ionization and collisional detachment processes

  12. Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

    Science.gov (United States)

    Sharif, M.; Kousar, Lubna

    2018-03-01

    This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordström black hole. We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles. We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole. The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole. The radial geodesic component starts decreasing in dyonic Reissner-Nordström black hole unlike Schwarzschild case. We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.

  13. Bianchi identities in higher dimensions

    International Nuclear Information System (INIS)

    Pravda, V; Pravdova, A; Coley, A; Milson, R

    2004-01-01

    A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension n. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in n - 4 spacelike dimensions or does not expand at all. It is shown that the existence of such principal geodesic null congruence in vacuum (together with an additional condition on twist) implies an algebraically special spacetime. We also use the Myers-Perry metric as an explicit example of a vacuum type D spacetime to show that principal geodesic null congruences in vacuum type D spacetimes do not share this property

  14. Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

    Science.gov (United States)

    Kassandrov, Vladimir V.; Rizcallah, Joseph A.

    We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.

  15. Automatically closing swing gate closure assembly

    Science.gov (United States)

    Chang, Shih-Chih; Schuck, William J.; Gilmore, Richard F.

    1988-01-01

    A swing gate closure assembly for nuclear reactor tipoff assembly wherein the swing gate is cammed open by a fuel element or spacer but is reliably closed at a desired closing rate primarily by hydraulic forces in the absence of a fuel charge.

  16. Upper limit on NUT charge from the observed terrestrial Sagnac effect

    Science.gov (United States)

    Kulbakova, A.; Karimov, R. Kh; Izmailov, R. N.; Nandi, K. K.

    2018-06-01

    The exact Sagnac delay in the Kerr–Taub–NUT (Newman–Unti–Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin , the delay does not vanish. This fact is similar to the non-vanishing of Lense–Thirring precession under even though the two effects originate from different premises. Assuming a reasonable input that the Kerr–Taub–NUT corrections are subsumed in the average residual uncertainty in the measured Sagnac delay, we compute upper limits on the NUT charge n. It is found that the upper limits on n are far larger than the Earth’s gravitational mass, which has not been detected in observations, implying that the Sagnac effect cannot constrain n to smaller values near zero. We find a curious difference between the delays for non-geodesic and geodesic clock orbits and point out its implication for the well known ‘twin paradox’ of special relativity.

  17. 76 FR 67498 - Post Office Closing

    Science.gov (United States)

    2011-11-01

    ... POSTAL REGULATORY COMMISSION [Docket No. A2012-17; Order No. 918] Post Office Closing AGENCY: Postal Regulatory Commission. ACTION: Notice. SUMMARY: This document informs the public that an appeal of the closing of the Venice, California post office has been filed. It identifies preliminary steps and...

  18. The evolution of magnetic structures due to open-quote open-quote magnetosonic streaming close-quote close-quote

    International Nuclear Information System (INIS)

    Ryutova, M.P.; Kaisig, M.; Tajima, T.

    1996-01-01

    The Faraday effect in gasdynamics called acoustic streaming and its accompanying nonlinear phenomena have analogies in plasma magnetohydrodynamics. A natural place where these effects may occur is the solar atmosphere with its strongly inhomogeneous magnetic fields concentrated in random magnetic flux tubes. Unlike acoustic streaming in the usual gasdynamics, nonlinear phenomena consisting in the generation of plasma flows by an oscillating magnetic flux tube, open-quote open-quote magnetosonic streaming close-quote close-quote (Ryutova 1986), is accompanied by a current drive and results in a specific evolution of magnetic structures: depending on the physical parameters of the medium a single magnetic flux tube may be either split into thinner flux tubes or dissolved diffusively into the ambient plasma. The effect of the open-quote open-quote magnetosonic streaming,close-quote close-quote on one hand, is an obvious candidate for the generation of mass flows at magnetic flux tubes sites, and on the other hand, it plays an essential role in the evolution of magnetic structures and ultimately may determine their lifetime. The theory of magnetosonic streaming is general and can be applied to other astrophysical objects that maintain oscillatory motions and contain structured magnetic fields or magnetic domains. We review analytical results and describe the origin of the magnetosonic streaming in magnetic flux tubes due to their interaction with acoustic waves. We study numerically the regime of the open-quote open-quote magnetosonic streaming close-quote close-quote corresponding to splitting of a magnetic flux tube. Our computer simulation supports and extends the analytical result. copyright 1996 The American Astronomical Society

  19. Energy conditions and spacetime singularities

    International Nuclear Information System (INIS)

    Tipler, F.J.

    1978-01-01

    In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete

  20. Closed Paths of Light Trapped in a Closed Fermat Curve

    Science.gov (United States)

    Dana-Picard, Thierry; Naiman, Aaron

    2002-01-01

    Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the…