Gravastars with higher dimensional spacetimes
Ghosh, Shounak; Ray, Saibal; Rahaman, Farook; Guha, B. K.
2018-07-01
We present a new model of gravastar in the higher dimensional Einsteinian spacetime including Einstein's cosmological constant Λ. Following Mazur and Mottola (2001, 2004) we design the star with three specific regions, as follows: (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact non-singular and stable solutions of the gravastar which seems physically very interesting and reasonable.
Spatial infinity in higher dimensional spacetimes
International Nuclear Information System (INIS)
Shiromizu, Tetsuya; Tomizawa, Shinya
2004-01-01
Motivated by recent studies on the uniqueness or nonuniqueness of higher dimensional black hole spacetime, we investigate the asymptotic structure of spatial infinity in n-dimensional spacetimes (n≥4). It turns out that the geometry of spatial infinity does not have maximal symmetry due to the nontrivial Weyl tensor (n-1) C abcd in general. We also address static spacetime and its multipole moments P a 1 a 2 ···a s . Contrasting with four dimensions, we stress that the local structure of spacetimes cannot be unique under fixed multipole moments in static vacuum spacetimes. For example, we consider the generalized Schwarzschild spacetimes which are deformed black hole spacetimes with the same multipole moments as spherical Schwarzschild black holes. To specify the local structure of the static vacuum solution we need some additional information, at least the Weyl tensor (n-2) C abcd at spatial infinity
Perturbations of higher-dimensional spacetimes
Energy Technology Data Exchange (ETDEWEB)
Durkee, Mark; Reall, Harvey S, E-mail: M.N.Durkee@damtp.cam.ac.uk, E-mail: H.S.Reall@damtp.cam.ac.uk [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2011-02-07
We discuss linearized gravitational perturbations of higher-dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric perturbation. These are the higher-dimensional generalizations of the 4D Newman-Penrose scalars that (in an algebraically special vacuum spacetime) satisfy decoupled equations of motion. We show that decoupling occurs in more than four dimensions if, and only if, the spacetime admits a null geodesic congruence with vanishing expansion, rotation and shear. Decoupling of electromagnetic perturbations occurs under the same conditions. Although these conditions are not satisfied in black hole spacetimes, they are satisfied in the near-horizon geometry of an extreme black hole.
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
Electromagnetic field in higher-dimensional black-hole spacetimes
International Nuclear Information System (INIS)
Krtous, Pavel
2007-01-01
A special test electromagnetic field in the spacetime of the higher-dimensional generally rotating NUT-(anti-)de Sitter black hole is found. It is adjusted to the hidden symmetries of the background represented by the principal Killing-Yano tensor. Such an electromagnetic field generalizes the field of charged black hole in four dimensions. In higher dimensions, however, the gravitational backreaction of such a field cannot be consistently solved
Naked singularities in higher dimensional Vaidya space-times
International Nuclear Information System (INIS)
Ghosh, S. G.; Dadhich, Naresh
2001-01-01
We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension
Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes
Schlue, Volker
2012-01-01
I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear wave equation on higher dimensional Schwarzschild black holes. I establish uniform energy decay and improved interior first order energy decay in all dimensions with rates in accordance with the 3 + 1-dimensional case. The method of proof departs from earlier work on th...
Euclidean scalar Green function in a higher dimensional global monopole space-time
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
2002-01-01
We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole space-time, i.e., a (1+d)-space-time with d≥3 which presents a solid angle deficit. Our result is expressed in terms of an infinite sum of products of Legendre functions with Gegenbauer polynomials. Although this Green function cannot be expressed in a closed form, for the specific case where the solid angle deficit is very small, it is possible to develop the sum and obtain the Green function in a more workable expression. Having this expression it is possible to calculate the vacuum expectation value of some relevant operators. As an application of this formalism, we calculate the renormalized vacuum expectation value of the square of the scalar field, 2 (x)> Ren , and the energy-momentum tensor, μν (x)> Ren , for the global monopole space-time with spatial dimensions d=4 and d=5
Generalized Uncertainty Principle and Black Hole Entropy of Higher-Dimensional de Sitter Spacetime
International Nuclear Information System (INIS)
Zhao Haixia; Hu Shuangqi; Zhao Ren; Li Huaifan
2007-01-01
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for four-dimensional spacetimes but also for higher-dimensional spacetimes. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.
International Nuclear Information System (INIS)
Froning, H. David; Meholic, Gregory V.
2010-01-01
This paper briefly explores higher dimensional spacetimes that extend Meholic's visualizable, fluidic views of: subluminal-luminal-superluminal flight; gravity, inertia, light quanta, and electromagnetism from 2-D to 3-D representations. Although 3-D representations have the potential to better model features of Meholic's most fundamental entities (Transluminal Energy Quantum) and of the zero-point quantum vacuum that pervades all space, the more complex 3-D representations loose some of the clarity of Meholic's 2-D representations of subluminal and superlumimal realms. So, much new work would be needed to replace Meholic's 2-D views of reality with 3-D ones.
Araneda, Bernardo
2018-04-01
We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.
Principal Killing strings in higher-dimensional Kerr-NUT-(A)dS spacetimes
Boos, Jens; Frolov, Valeri P.
2018-04-01
We construct special solutions of the Nambu-Goto equations for stationary strings in a general Kerr-NUT-(A)dS spacetime in any number of dimensions. This construction is based on the existence of explicit and hidden symmetries generated by the principal tensor which exists for these metrics. The characteristic property of these string configurations, which we call "principal Killing strings," is that they are stretched out from "infinity" to the horizon of the Kerr-NUT-(A)dS black hole and remain regular at the latter. We also demonstrate that principal Killing strings extract angular momentum from higher-dimensional rotating black holes and interpret this as the action of an asymptotic torque.
Riccion from higher-dimensional space-time with D-dimensional ...
Indian Academy of Sciences (India)
suggest that space-time above 3 05¢1016 GeV should be fractal. .... Here VD is the volume of SD, g´4·Dµ is the determinant of the metric tensor gMN (M ...... means that above 3.05x1016 GeV, SD is not a smooth surface whereas M4 is smooth.
Late-time tails of wave propagation in higher dimensional spacetimes
International Nuclear Information System (INIS)
Cardoso, Vitor; Yoshida, Shijun; Dias, Oscar J.C.; Lemos, Jose P.S.
2003-01-01
We study the late-time tails appearing in the propagation of massless fields (scalar, electromagnetic, and gravitational) in the vicinities of a D-dimensional Schwarzschild black hole. We find that at late times the fields always exhibit a power-law falloff, but the power law is highly sensitive to the dimensionality of the spacetime. Accordingly, for odd D>3 we find that the field behaves as t -(2l+D-2) at late times, where l is the angular index determining the angular dependence of the field. This behavior is entirely due to D being odd; it does not depend on the presence of a black hole in the spacetime. Indeed this tail is already present in the flat space Green's function. On the other hand, for even D>4 the field decays as t -(2l+3D-8) , and this time there is no contribution from the flat background. This power law is entirely due to the presence of the black hole. The D=4 case is special and exhibits, as is well known, t -(2l+3) behavior. In the extra dimensional scenario for our Universe, our results are strictly correct if the extra dimensions are infinite, but also give a good description of the late-time behavior of any field if the large extra dimensions are large enough
Charged particle in higher dimensional weakly charged rotating black hole spacetime
International Nuclear Information System (INIS)
Frolov, Valeri P.; Krtous, Pavel
2011-01-01
We study charged particle motion in weakly charged higher dimensional black holes. To describe the electromagnetic field we use a test field approximation and the higher dimensional Kerr-NUT-(A)dS metric as a background geometry. It is shown that for a special configuration of the electromagnetic field, the equations of motion of charged particles are completely integrable. The vector potential of such a field is proportional to one of the Killing vectors (called a primary Killing vector) from the 'Killing tower' of symmetry generating objects which exists in the background geometry. A free constant in the definition of the adopted electromagnetic potential is proportional to the electric charge of the higher dimensional black hole. The full set of independent conserved quantities in involution is found. We demonstrate that Hamilton-Jacobi equations are separable, as is the corresponding Klein-Gordon equation and its symmetry operators.
On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Pravda, Vojtěch; Pravdová, Alena
Roč. 35, č. 7 ( 2018 ), č. článku 075004. ISSN 0264-9381 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * WANDs * Weyl tensor Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 3.119, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6382/aaae25
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.
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2003-01-01
The free energy and entropy of Reissner-Nordstrom black holes in higher-dimensional space-time are calculated by the quantum statistic method with a brick wall model. The space-time of the black holes is divided into three regions: region 1, (r > r0); region 2, (r0 > r > n); and region 3, (T-J > r > 0), where r0 is the radius of the outer event horizon, and r, is the radius of the inner event horizon. Detailed calculation shows that the entropy contributed by region 2 is zero, the entropy contributed by region 1 is positive and proportional to the outer event horizon area, the entropy contributed by region 3 is negative and proportional to the inner event horizon area. The total entropy contributed by all the three regions is positive and proportional to the area difference between the outer and inner event horizons. As rt approaches r0 in the nearly extreme case, the total quantum statistical entropy approaches zero.
Exact solutions of Einstein and Einstein-Maxwell equations in higher-dimensional spacetime
International Nuclear Information System (INIS)
Xu Dianyan; Beijing Univ., BJ
1988-01-01
The D-dimensional Schwarzschild-de Sitter metric and Reissner-Nordstrom-de-Sitter metric are derived directly by solving the Einstein and Einstein-Maxwell equations. The D-dimensional Kerr metric is rederived by using the complex coordinate transformation method and the D-dimensional Kerr-de Sitter metric is also given. The conjecture about the D-dimensional metric of a rotating charged mass is given at the end of this paper. (author)
International Nuclear Information System (INIS)
Nariai, Hidekazu; Ishihara, Hideki.
1983-01-01
Various geometrical properties of Nariai's less-familiar solution of the vacuum Einstein equations R sub( mu nu ) = lambda g sub( mu nu ) is f irst summarized in comparison with de Sitter's well-known solution. Next an extension of both solutions is performed in a six-dimensional space on the supposition that such an extension will in future become useful to elucidate more closely the creation of particles in an inflationary stage of the big-bang universe. For preparation, the behavior of a massive scalar field in the extended space-time is studied in a classical level. (author)
Some spacetimes with higher rank Killing-Staeckel tensors
International Nuclear Information System (INIS)
Gibbons, G.W.; Houri, T.; Kubiznak, D.; Warnick, C.M.
2011-01-01
By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime.
International Nuclear Information System (INIS)
Spinelly, J.; Mello, E.R. Bezerra de
2008-01-01
In this paper we investigate the vacuum polarization effects associated with quantum fermionic charged fields in a generalized (d+1)-dimensional cosmic string space-times considering the presence of a magnetic flux along the string. In order to develop this analysis we calculate a general expression for the respective Green function, valid for several different values of d, which is expressed in terms of a bispinor associated with the square of the Dirac operator. Adopting this result, we explicitly calculate the renormalized vacuum expectation values of the energy-momentum tensors, (T A B ) Ren. , associated with massless fields. Moreover, for specific values of the parameters which codify the cosmic string and the fractional part of the ratio of the magnetic flux by the quantum one, we were able to present in closed forms the bispinor and the respective Green function for massive fields.
Inflationary scenario from higher curvature warped spacetime
International Nuclear Information System (INIS)
Banerjee, Narayan; Paul, Tanmoy
2017-01-01
We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR 2 in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n s ) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)
Inflationary scenario from higher curvature warped spacetime
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Narayan [Indian Institute of Science Education and Research Kolkata, Department of Physical Sciences, Nadia, West Bengal (India); Paul, Tanmoy [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2017-10-15
We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR{sup 2} in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n{sub s}) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)
Radion stabilization in higher curvature warped spacetime
Energy Technology Data Exchange (ETDEWEB)
Das, Ashmita [Indian Institute of Technology, Department of Physics, Guwahati, Assam (India); Mukherjee, Hiya; Paul, Tanmoy; SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2018-02-15
We consider a five dimensional AdS spacetime in presence of higher curvature term like F(R) = R + αR{sup 2} in the bulk. In this model, we examine the possibility of modulus stabilization from the scalar degrees of freedom of higher curvature gravity free of ghosts. Our result reveals that the model stabilizes itself and the mechanism of modulus stabilization can be argued from a geometric point of view. We determine the region of the parametric space for which the modulus (or radion) can to be stabilized. We also show how the mass and coupling parameters of radion field are modified due to higher curvature term leading to modifications of its phenomenological implications on the visible 3-brane. (orig.)
Higher dimensional loop quantum cosmology
International Nuclear Information System (INIS)
Zhang, Xiangdong
2016-01-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n + 1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n + 1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n + 1 dimensional model and the 3 + 1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology. (orig.)
Maximal slicing of D-dimensional spherically symmetric vacuum spacetime
International Nuclear Information System (INIS)
Nakao, Ken-ichi; Abe, Hiroyuki; Yoshino, Hirotaka; Shibata, Masaru
2009-01-01
We study the foliation of a D-dimensional spherically symmetric black-hole spacetime with D≥5 by two kinds of one-parameter families of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpetlike shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces avoid the singularity irrespective of the dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of D=5, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. These data will be useful for checking five-dimensional numerical-relativity codes based on the moving puncture approach.
Topology and incompleteness for 2+1-dimensional cosmological spacetimes
Fajman, David
2017-06-01
We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.
Higher-dimensional Bianchi type-VIh cosmologies
Lorenz-Petzold, D.
1985-09-01
The higher-dimensional perfect fluid equations of a generalization of the (1 + 3)-dimensional Bianchi type-VIh space-time are discussed. Bianchi type-V and Bianchi type-III space-times are also included as special cases. It is shown that the Chodos-Detweiler (1980) mechanism of cosmological dimensional-reduction is possible in these cases.
The space-time model according to dimensional continuous space-time theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2014-01-01
This article results from the Dimensional Continuous Space-Time Theory for which the introductory theoretician was presented in [1]. A theoretical model of the Continuous Space-Time is presented. The wave equation of time into absolutely stationary empty space referential will be described in detail. The complex time, that is the time fixed on the infinite phase time speed referential, is deduced from the New View of Relativity Theory that is being submitted simultaneously with this article in this congress. Finally considering the inseparable Space-Time is presented the duality equation wave-particle.
Heat engine in the three-dimensional spacetime
Energy Technology Data Exchange (ETDEWEB)
Mo, Jie-Xiong [Institute of Theoretical Physics, Lingnan Normal University,Zhanjiang, 524048, Guangdong (China); Department of Physics, Lingnan Normal University,Zhanjiang, 524048, Guangdong (China); Liang, Feng [Department of Physics, Lingnan Normal University,Zhanjiang, 524048, Guangdong (China); Li, Gu-Qiang [Institute of Theoretical Physics, Lingnan Normal University,Zhanjiang, 524048, Guangdong (China); Department of Physics, Lingnan Normal University,Zhanjiang, 524048, Guangdong (China)
2017-03-02
We define a kind of heat engine via three-dimensional charged BTZ black holes. This case is quite subtle and needs to be more careful. The heat flow along the isochores does not equal to zero since the specific heat C{sub V}≠0 and this point completely differs from the cases discussed before whose isochores and adiabats are identical. So one cannot simply apply the paradigm in the former literatures. However, if one introduces a new thermodynamic parameter associated with the renormalization length scale, the above problem can be solved. We obtain the analytical efficiency expression of the three-dimensional charged BTZ black hole heat engine for two different schemes. Moreover, we double check with the exact formula. Our result presents the first specific example for the sound correctness of the exact efficiency formula. We argue that the three-dimensional charged BTZ black hole can be viewed as a toy model for further investigation of holographic heat engine. Furthermore, we compare our result with that of the Carnot cycle and extend the former result to three-dimensional spacetime. In this sense, the result in this paper would be complementary to those obtained in four-dimensional spacetime or ever higher. Last but not the least, the heat engine efficiency discussed in this paper may serve as a criterion to discriminate the two thermodynamic approaches introduced in ref. https://www.doi.org/10.1103/PhysRevD.92.124069 and our result seems to support the approach which introduces a new thermodynamic parameter R=r{sub 0}.
Energy Technology Data Exchange (ETDEWEB)
Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)
2014-12-01
In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)
Stationary closed strings in five-dimensional flat spacetime
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.
Higher-dimensional relativistic-fluid spheres
International Nuclear Information System (INIS)
Patel, L. K.; Ahmedabad, Gujarat Univ.
1997-01-01
They consider the hydrostatic equilibrium of relativistic-fluid spheres for a D-dimensional space-time. Three physically viable interior solutions of the Einstein field equations corresponding to perfect-fluid spheres in a D-dimensional space-time are obtained. When D = 4 they reduce to the Tolman IV solution, the Mehra solution and the Finch-Skea solution. The solutions are smoothly matched with the D-dimensional Schwarzschild exterior solution at the boundary r = a of the fluid sphere. Some physical features and other related details of the solutions are briefly discussed. A brief description of two other new solutions for higher-dimensional perfect-fluid spheres is also given
Spinor calculus on 5-dimensional spacetimes
International Nuclear Information System (INIS)
Gomez-Lobo, Alfonso Garcia-Parrado; Martin-Garcia, Jose M
2010-01-01
We explain how Penrose's spinor calculus of 4-dimensional Lorentzian geometry is implemented in a 5-dimensional Lorentzian manifold. A number of issues, such as the essential spin algebra, the spin covariant derivative and the algebro-differential properties of the curvature spinors are discussed.
Constant scalar curvature hypersurfaces in (3 + 1) -dimensional GHMC Minkowski spacetimes
Smith, Graham
2018-06-01
We prove that every (3 + 1) -dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In other words, we prove that every such spacetime carries a unique time function with isochrones of constant scalar curvature. Furthermore, this time function is a smooth submersion.
The Validity of Dimensional Regularization Method on Fractal Spacetime
Directory of Open Access Journals (Sweden)
Yong Tao
2013-01-01
Full Text Available Svozil developed a regularization method for quantum field theory on fractal spacetime (1987. Such a method can be applied to the low-order perturbative renormalization of quantum electrodynamics but will depend on a conjectural integral formula on non-integer-dimensional topological spaces. The main purpose of this paper is to construct a fractal measure so as to guarantee the validity of the conjectural integral formula.
Exact interior solutions in 2 + 1-dimensional spacetime
Energy Technology Data Exchange (ETDEWEB)
Rahaman, Farook; Bhar, Piyali [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Biswas, Ritabrata [Indian Institute of Engineering Sceince and Technology Shibpur, Howrah, West Bengal (India); Usmani, A.A. [Aligarh Muslim University, Department of Physics, Aligarh, Uttar Pradesh (India)
2014-04-15
We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)
Quantum vacuum energy in two dimensional space-times
International Nuclear Information System (INIS)
Davies, P.C.W.; Fulling, S.A.
1977-01-01
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed. (author)
Quantum vacuum energy in two dimensional space-times
Energy Technology Data Exchange (ETDEWEB)
Davies, P C.W.; Fulling, S A [King' s Coll., London (UK). Dept. of Mathematics
1977-04-21
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed.
Electromagnetic-field equations in the six-dimensional space-time R6
International Nuclear Information System (INIS)
Teli, M.T.; Palaskar, D.
1984-01-01
Maxwell's equations (without monopoles) for electromagnetic fields are obtained in six-dimensional space-time. The equations possess structural symmetry in space and time, field and source densities. Space-time-symmetric conservation laws and field solutions are obtained. The results are successfully correlated with their four-dimensional space-time counterparts
Introducing the Dimensional Continuous Space-Time Theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2013-01-01
This article is an introduction to a new theory. The name of the theory is justified by the dimensional description of the continuous space-time of the matter, energy and empty space, that gathers all the real things that exists in the universe. The theory presents itself as the consolidation of the classical, quantum and relativity theories. A basic equation that describes the formation of the Universe, relating time, space, matter, energy and movement, is deduced. The four fundamentals physics constants, light speed in empty space, gravitational constant, Boltzmann's constant and Planck's constant and also the fundamentals particles mass, the electrical charges, the energies, the empty space and time are also obtained from this basic equation. This theory provides a new vision of the Big-Bang and how the galaxies, stars, black holes and planets were formed. Based on it, is possible to have a perfect comprehension of the duality between wave-particle, which is an intrinsic characteristic of the matter and energy. It will be possible to comprehend the formation of orbitals and get the equationing of atomics orbits. It presents a singular comprehension of the mass relativity, length and time. It is demonstrated that the continuous space-time is tridimensional, inelastic and temporally instantaneous, eliminating the possibility of spatial fold, slot space, worm hole, time travels and parallel universes. It is shown that many concepts, like dark matter and strong forces, that hypothetically keep the cohesion of the atomics nucleons, are without sense.
Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime
Institute of Scientific and Technical Information of China (English)
2008-01-01
The generalized uncertainty relation is introduced to calculate the quantum statis-tical entropy corresponding to cosmic horizon. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical en-tropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon is the entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.
Quantum theory of spinor field in four-dimensional Riemannian space-time
International Nuclear Information System (INIS)
Shavokhina, N.S.
1996-01-01
The review deals with the spinor field in the four-dimensional Riemannian space-time. The field beys the Dirac-Fock-Ivanenko equation. Principles of quantization of the spinor field in the Riemannian space-time are formulated which in a particular case of the plane space-time are equivalent to the canonical rules of quantization. The formulated principles are exemplified by the De Sitter space-time. The study of quantum field theory in the De Sitter space-time is interesting because it itself leads to a method of an invariant well for plane space-time. However, the study of the quantum spinor field theory in an arbitrary Riemannian space-time allows one to take into account the influence of the external gravitational field on the quantized spinor field. 60 refs
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
Energy Technology Data Exchange (ETDEWEB)
Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)
2017-12-15
We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)
We live in the quantum 4-dimensional Minkowski space-time
Hwang, W-Y. Pauchy
2015-01-01
We try to define "our world" by stating that "we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge group $SU_c(3) \\times SU_L(2) \\times U(1) \\times SU_f(3)$ built-in from the outset". We begin by explaining what "space" and "time" are meaning for us - the 4-dimensional Minkowski space-time, then proceeding to the quantum 4-dimensional Minkowski space-time. In our world, there are fields, or, point-like particles. Particle physics is described by the so-called ...
Spacetimes of Weyl and Ricci type N in higher dimensions
International Nuclear Information System (INIS)
Kuchynka, M; Pravdová, A
2016-01-01
We study the geometrical properties of null congruences generated by an aligned null direction of the Weyl tensor (WAND) in spacetimes of Weyl and Ricci type N (possibly with a non-vanishing cosmological constant) in an arbitrary dimension. We prove that a type N Ricci tensor and a type III or N Weyl tensor have to be aligned. In such spacetimes, the multiple WAND has to be geodetic. For spacetimes with type N aligned Weyl and Ricci tensors, the canonical form of the optical matrix in the twisting and non-twisting cases is derived and the dependence of the Weyl and the Ricci tensors and Ricci rotation coefficients on the affine parameter of the geodetic null congruence generated by the WAND is obtained. (paper)
Fermion tunneling from higher-dimensional black holes
International Nuclear Information System (INIS)
Lin Kai; Yang Shuzheng
2009-01-01
Via the semiclassical approximation method, we study the 1/2-spin fermion tunneling from a higher-dimensional black hole. In our work, the Dirac equations are transformed into a simple form, and then we simplify the fermion tunneling research to the study of the Hamilton-Jacobi equation in curved space-time. Finally, we get the fermion tunneling rates and the Hawking temperatures at the event horizon of higher-dimensional black holes. We study fermion tunneling of a higher-dimensional Schwarzschild black hole and a higher-dimensional spherically symmetric quintessence black hole. In fact, this method is also applicable to the study of fermion tunneling from four-dimensional or lower-dimensional black holes, and we will take the rainbow-Finsler black hole as an example in order to make the fact explicit.
Eruptive Massive Vector Particles of 5-Dimensional Kerr-Gödel Spacetime
Övgün, A.; Sakalli, I.
2018-02-01
In this paper, we investigate Hawking radiation of massive spin-1 particles from 5-dimensional Kerr-Gödel spacetime. By applying the WKB approximation and the Hamilton-Jacobi ansatz to the relativistic Proca equation, we obtain the quantum tunneling rate of the massive vector particles. Using the obtained tunneling rate, we show how one impeccably computes the Hawking temperature of the 5-dimensional Kerr-Gödel spacetime.
Geometry of higher-dimensional black hole thermodynamics
International Nuclear Information System (INIS)
Aaman, Jan E.; Pidokrajt, Narit
2006-01-01
We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta
Casimir energy density for spherical universes in n-dimensional spacetime
International Nuclear Information System (INIS)
Oezcan, Mustafa
2006-01-01
We consider the Casimir effect for the massless conformal scalar field in an n-dimensional, closed, static universe. We calculate the renormalized vacuum energy density using the covariant point-splitting method, the mode-sum regularization and the renormalized vacuum energy with the zeta-function regularization. We observe that all odd spacetime dimensions give us the zero renormalized vacuum energy density. For even spacetime dimensions the renormalized vacuum energy density oscillates in sign. The result agrees with three regularization techniques. The Casimir energy density for spherical universes in n-dimensional spacetime is regarded as interesting both to understand the correspondence between the sign of the effect and the dimension of manifold in topology and as a key to confirming the Casimir energy for half spherical universes (manifold with boundary) in n-dimensional spacetime
International Nuclear Information System (INIS)
Witek, Helvi; Nerozzi, Andrea; Zilhao, Miguel; Herdeiro, Carlos; Gualtieri, Leonardo; Cardoso, Vitor; Sperhake, Ulrich
2010-01-01
Higher dimensional black holes play an exciting role in fundamental physics, such as high energy physics. In this paper, we use the formalism and numerical code reported in [1] to study the head-on collision of two black holes. For this purpose we provide a detailed treatment of gravitational wave extraction in generic D dimensional space-times, which uses the Kodama-Ishibashi formalism. For the first time, we present the results of numerical simulations of the head-on collision in five space-time dimensions, together with the relevant physical quantities. We show that the total radiated energy, when two black holes collide from rest at infinity, is approximately (0.089±0.006)% of the center of mass energy, slightly larger than the 0.055% obtained in the four-dimensional case, and that the ringdown signal at late time is in very good agreement with perturbative calculations.
Instabilities of higher dimensional compactifications
International Nuclear Information System (INIS)
Accetta, F.S.
1987-02-01
Various schemes for cosmological compactification of higher dimensional theories are considered. Possible instabilities which drive the ground state with static internal space to de Sitter-like expansion of all dimensions are discussed. These instabilities are due to semiclassical barrier penetration and classical thermal fluctuations. For the case of the ten dimensional Chapline-Manton action, it is possible to avoid such difficulties by balancing one-loop Casimir corrections against monopole contributions from the field strength H/sub MNP/ and fermionic condensates. 10 refs
Torsion and curvature in higher dimensional supergravity theories
International Nuclear Information System (INIS)
Smith, A.W.; Pontificia Univ. Catolica do Rio de Janeiro
1983-01-01
This work is an extension of Dragon's theorems to higher dimensional space-time. It is shown that the first set of Bianchi identities allow us to express the curvature components in terms of torsion components and its covariant derivatives. It is also shown that the second set of Bianchi identities does not give any new information which is not already contained in the first one. (Author) [pt
Moduli stabilization in higher dimensional brane models
International Nuclear Information System (INIS)
Flachi, Antonino; Pujolas, Oriol; Garriga, Jaume; Tanaka, Takahiro
2003-01-01
We consider a class of warped higher dimensional brane models with topology M x Σ x S 1 /Z 2 , where Σ is a D2 dimensional manifold. Two branes of co-dimension one are embedded in such a bulk space-time and sit at the orbifold fixed points. We concentrate on the case where an exponential warp factor (depending on the distance along the orbifold) accompanies the Minkowski M and the internal space Σ line elements. We evaluate the moduli effective potential induced by bulk scalar fields in these models, and we show that generically this can stabilize the size of the extra dimensions. As an application, we consider a scenario where supersymmetry is broken not far below the cutoff scale, and the hierarchy between the electroweak and the effective Planck scales is generated by a combination of redshift and large volume effects. The latter is efficient due to the shrinking of Σ at the negative tension brane, where matter is placed. In this case, we find that the effective potential can stabilize the size of the extra dimensions (and the hierarchy) without fine tuning, provided that the internal space Σ is flat. (author)
Moduli stabilization in higher dimensional brane models
Energy Technology Data Exchange (ETDEWEB)
Flachi, Antonino; Pujolas, Oriol [IFAE, Campus UAB, 08193 Bellaterra, Barcelona (Spain)]. E-mail: pujolas@ifae.es; Garriga, Jaume [IFAE, Campus UAB, 08193 Bellaterra, Barcelona (Spain); Departament de Fisica Fonamental and C.E.R. en Astrofisica, Fisica de Particules i Cosmologia Universitat de Barcelona, Marti i Franques 1, 08028 Barcelona (Spain); Tanaka, Takahiro [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford MA 02155 (United States); Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2003-08-01
We consider a class of warped higher dimensional brane models with topology M x {sigma} x S{sup 1}/Z{sub 2}, where {sigma} is a D2 dimensional manifold. Two branes of co-dimension one are embedded in such a bulk space-time and sit at the orbifold fixed points. We concentrate on the case where an exponential warp factor (depending on the distance along the orbifold) accompanies the Minkowski M and the internal space {sigma} line elements. We evaluate the moduli effective potential induced by bulk scalar fields in these models, and we show that generically this can stabilize the size of the extra dimensions. As an application, we consider a scenario where supersymmetry is broken not far below the cutoff scale, and the hierarchy between the electroweak and the effective Planck scales is generated by a combination of redshift and large volume effects. The latter is efficient due to the shrinking of {sigma} at the negative tension brane, where matter is placed. In this case, we find that the effective potential can stabilize the size of the extra dimensions (and the hierarchy) without fine tuning, provided that the internal space {sigma} is flat. (author)
Higher dimensional discrete Cheeger inequalities
Directory of Open Access Journals (Sweden)
Anna Gundert
2015-01-01
Full Text Available For graphs there exists a strong connection between spectral and combinatorial expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the lower bound of which states that $\\lambda(G \\leq h(G$, where $\\lambda(G$ is the second smallest eigenvalue of the Laplacian of a graph $G$ and $h(G$ is the Cheeger constant measuring the edge expansion of $G$. We are interested in generalizations of expansion properties to finite simplicial complexes of higher dimension (or uniform hypergraphs. Whereas higher dimensional Laplacians were introduced already in 1945 by Eckmann, the generalization of edge expansion to simplicial complexes is not straightforward. Recently, a topologically motivated notion analogous to edge expansion that is based on $\\mathbb{Z}_2$-cohomology was introduced by Gromov and independently by Linial, Meshulam and Wallach. It is known that for this generalization there is no direct higher dimensional analogue of the lower bound of the Cheeger inequality. A different, combinatorially motivated generalization of the Cheeger constant, denoted by $h(X$, was studied by Parzanchevski, Rosenthal and Tessler. They showed that indeed $\\lambda(X \\leq h(X$, where $\\lambda(X$ is the smallest non-trivial eigenvalue of the ($(k-1$-dimensional upper Laplacian, for the case of $k$-dimensional simplicial complexes $X$ with complete $(k-1$-skeleton. Whether this inequality also holds for $k$-dimensional complexes with non-com\\-plete$(k-1$-skeleton has been an open question.We give two proofs of the inequality for arbitrary complexes. The proofs differ strongly in the methods and structures employed,and each allows for a different kind of additional strengthening of the original result.
Lorentz covariant tempered distributions in two-dimensional space-time
International Nuclear Information System (INIS)
Zinov'ev, Yu.M.
1989-01-01
The problem of describing Lorentz covariant distributions without any spectral condition has hitherto remained unsolved even for two-dimensional space-time. Attempts to solve this problem have already been made. Zharinov obtained an integral representation for the Laplace transform of Lorentz invariant distributions with support in the product of two-dimensional future light cones. However, this integral representation does not make it possible to obtain a complete description of the corresponding Lorentz invariant distributions. In this paper the author gives a complete description of Lorentz covariant distributions for two-dimensional space-time. No spectral conditions is assumed
International Nuclear Information System (INIS)
Santos, Nuno Loureiro; Dias, Oscar J.C.; Lemos, Jose P.S.
2004-01-01
We study the matching between the Hawking temperature of a large class of static D-dimensional black holes and the Unruh temperature of the corresponding higher dimensional Rindler spacetime. In order to accomplish this task we find the global embedding of the D-dimensional black holes into a higher dimensional Minkowskian spacetime, called the global embedding Minkowskian spacetime procedure (GEMS procedure). These global embedding transformations are important on their own, since they provide a powerful tool that simplifies the study of black hole physics by working instead, but equivalently, in an accelerated Rindler frame in a flat background geometry. We discuss neutral and charged Tangherlini black holes with and without cosmological constant, and in the negative cosmological constant case, we consider the three allowed topologies for the horizons (spherical, cylindrical/toroidal, and hyperbolic)
International Nuclear Information System (INIS)
Elizalde, E.; Odintsov, S.D.; Romeo, A.
1995-01-01
We develop a general formalism to study the renormalization-group- (RG-)improved effective potential for renormalizable gauge theories, including matter-R 2 -gravity, in curved spacetime. The result is given up to quadratic terms in curvature, and one-loop effective potentials may be easily obtained from it. As an example, we consider scalar QED, where dimensional transmutation in curved space and the phase structure of the potential (in particular, curvature-induced phase transitions) are discussed. For scalar QED with higher-derivative quantum gravity (QG), we examine the influence of QG on dimensional transmutation and calculate QG corrections to the scalar-to-vector mass ratio. The phase structure of the RG-improved effective potential is also studied in this case, and the values of the induced Newton and cosmological coupling constants at the critical point are estimated. The stability of the running scalar coupling in the Yukawa theory with conformally invariant higher-derivative QG, and in the standard model with the same addition, is numerically analyzed. We show that, in these models, QG tends to make the scalar sector less unstable
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.
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.
Dirac equation in 5- and 6-dimensional curved space-time manifolds
International Nuclear Information System (INIS)
Vladimirov, Yu.S.; Popov, A.D.
1984-01-01
The program of plotting unified multidimensional theory of gravitation, electromagnetism and electrically charged matter with transition from 5-dimensional variants to 6-dimensional theory possessing signature (+----+) is developed. For recording the Dirac equation in 5- and 6-dimensional curved space-time manifolds the tetrad formalism and γ-matrix formulation of the General Relativity Theory are used. It is shown that the 6-dimensional theory case unifies the two private cases of 5-dimensional theory and corresponds to two possibilities of the theory developed by Kadyshevski
A higher order space-time Galerkin scheme for time domain integral equations
Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam
2014-01-01
Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.
On Maximal Surfaces in Certain Non-Flat 3-Dimensional Robertson-Walker Spacetimes
Energy Technology Data Exchange (ETDEWEB)
Romero, Alfonso, E-mail: aromero@ugr.es [Universidad de Granada, Departamento de Geometria y Topologia (Spain); Rubio, Rafael M., E-mail: rmrubio@uco.es [Universidad de Cordoba, Departamento de Matematicas, Campus de Rabanales (Spain)
2012-09-15
An upper bound for the integral, on a geodesic disc, of the squared length of the gradient of a distinguished function on any maximal surface in certain non-flat 3-dimensional Robertson-Walker spacetimes is obtained. As an application, a new proof of a known Calabi-Bernstein's theorem is given.
Quantum theory of string in the four-dimensional space-time
International Nuclear Information System (INIS)
Pron'ko, G.P.
1986-01-01
The Lorentz invariant quantum theory of string is constructed in four-dimensional space-time. Unlike the traditional approach whose result was breaking of Lorentz invariance, our method is based on the usage of other variables for description of string configurations. The method of an auxiliary spectral problem for periodic potentials is the main tool in construction of these new variables
Collapsing perfect fluid in self-similar five dimensional space-time and cosmic censorship
International Nuclear Information System (INIS)
Ghosh, S.G.; Sarwe, S.B.; Saraykar, R.V.
2002-01-01
We investigate the occurrence and nature of naked singularities in the gravitational collapse of a self-similar adiabatic perfect fluid in a five dimensional space-time. The naked singularities are found to be gravitationally strong in the sense of Tipler and thus violate the cosmic censorship conjecture
Nonrenormalizable quantum field models in four-dimensional space-time
International Nuclear Information System (INIS)
Raczka, R.
1978-01-01
The construction of no-cutoff Euclidean Green's functions for nonrenormalizable interactions L/sub I/(phi) = lambda∫ddelta (epsilon): expepsilonphi: in four-dimensional space-time is carried out. It is shown that all axioms for the generating functional of the Euclidean Green's function are satisfied except perhaps SO(4) invariance
Spacetimes of Weyl and Ricci type N in higher dimensions
Czech Academy of Sciences Publication Activity Database
Kuchynka, M.; Pravdová, Alena
2016-01-01
Roč. 33, č. 11 (2016), s. 115006 ISSN 0264-9381 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : Weyl type N * Ricci type N * higher dimensions Subject RIV: BA - General Mathematics Impact factor: 3.119, year: 2016 http://iopscience.iop.org/article/10.1088/0264-9381/33/11/115006
Area spectrum of the D-dimensional de Sitter spacetime
International Nuclear Information System (INIS)
Lopez-Ortega, A.
2009-01-01
The determination of the quantum area spectrum of a black hole horizon by means of its asymptotic quasinormal frequencies has been explored recently. We believe that for D-dimensional de Sitter horizon we must study if the idea works. Thus taking into account the local description of the thermodynamics of horizons proposed by Padmanabhan and the results of Hod, Kunstatter, and Maggiore we study the area spectrum of the D-dimensional de Sitter horizon.
Area spectrum of the D-dimensional de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Lopez-Ortega, A., E-mail: alopezo@ipn.m [Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada, Unidad Legaria, Instituto Politecnico Nacional, Calzada Legaria 694 Colonia Irrigacion, Delegacion Miguel Hidalgo, Mexico, D.F., C.P. 11500 (Mexico)
2009-11-23
The determination of the quantum area spectrum of a black hole horizon by means of its asymptotic quasinormal frequencies has been explored recently. We believe that for D-dimensional de Sitter horizon we must study if the idea works. Thus taking into account the local description of the thermodynamics of horizons proposed by Padmanabhan and the results of Hod, Kunstatter, and Maggiore we study the area spectrum of the D-dimensional de Sitter horizon.
Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model
Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.
2018-04-01
We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.
On renormalisation of the quantum stress tensor in curved space-time by dimensional regularisation
International Nuclear Information System (INIS)
Bunch, T.S.
1979-01-01
Using dimensional regularisation, a prescription is given for obtaining a finite renormalised stress tensor in curved space-time. Renormalisation is carried out by renormalising coupling constants in the n-dimensional Einstein equation generalised to include tensors which are fourth order in derivatives of the metric. Except for the special case of a massless conformal field in a conformally flat space-time, this procedure is not unique. There exists an infinite one-parameter family of renormalisation ansatze differing from each other in the finite renormalisation that takes place. Nevertheless, the renormalised stress tensor for a conformally invariant field theory acquires a nonzero trace which is independent of the renormalisation ansatz used and which has a value in agreement with that obtained by other methods. A comparison is made with some earlier work using dimensional regularisation which is shown to be in error. (author)
Thermodynamics of (d+1)-dimensional NUT-charged AdS spacetimes
International Nuclear Information System (INIS)
Clarkson, R.; Fatibene, L.; Mann, R.B.
2003-01-01
We consider the thermodynamic properties of (d+1)-dimensional spacetimes with NUT charges. Such spacetimes are asymptotically locally anti-de Sitter (or flat), with non-trivial topology in their spatial sections, and can have fixed point sets of the Euclidean time symmetry that are either (d-1)-dimensional (called 'bolts') or of lower dimensionality (pure 'NUTs'). We compute the free energy, conserved mass, and entropy for 4, 6, 8 and 10 dimensions for each, using both Noether charge methods and the AdS/CFT-inspired counterterm approach. We then generalize these results to arbitrary dimensionality. We find in 4k+2 dimensions that there are no regions in parameter space in the pure NUT case for which the entropy and specific heat are both positive, and so all such spacetimes are thermodynamically unstable. For the pure NUT case in 4k dimensions a region of stability exists in parameter space that decreases in size with increasing dimensionality. All bolt cases have some region of parameter space for which thermodynamic stability can be realized
Possibility of higher-dimensional anisotropic compact star
International Nuclear Information System (INIS)
Bhar, Piyali; Rahaman, Farook; Ray, Saibal; Chatterjee, Vikram
2015-01-01
We provide a new class of interior solutions for anisotropic stars admitting conformal motion in higher-dimensional noncommutative spacetime. The Einstein field equations are solved by choosing a particular density distribution function of Lorentzian type as provided by Nazari and Mehdipour [1, 2] under a noncommutative geometry. Several cases with 4 and higher dimensions, e.g. 5, 6, and 11 dimensions, are discussed separately. An overall observation is that the model parameters, such as density, radial pressure, transverse pressure, and anisotropy, all are well behaved and represent a compact star with mass 2.27 M s un and radius 4.17 km. However, emphasis is put on the acceptability of the model from a physical point of view. As a consequence it is observed that higher dimensions, i.e. beyond 4D spacetime, exhibit several interesting yet bizarre features, which are not at all untenable for a compact stellar model of strange quark type; thus this dictates the possibility of its extra-dimensional existence. (orig.)
Possibility of higher-dimensional anisotropic compact star
Energy Technology Data Exchange (ETDEWEB)
Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India); Chatterjee, Vikram [Central Footwear Training Centre, Department of Physics, Parganas, West Bengal (India)
2015-05-15
We provide a new class of interior solutions for anisotropic stars admitting conformal motion in higher-dimensional noncommutative spacetime. The Einstein field equations are solved by choosing a particular density distribution function of Lorentzian type as provided by Nazari and Mehdipour [1, 2] under a noncommutative geometry. Several cases with 4 and higher dimensions, e.g. 5, 6, and 11 dimensions, are discussed separately. An overall observation is that the model parameters, such as density, radial pressure, transverse pressure, and anisotropy, all are well behaved and represent a compact star with mass 2.27 M{sub s}un and radius 4.17 km. However, emphasis is put on the acceptability of the model from a physical point of view. As a consequence it is observed that higher dimensions, i.e. beyond 4D spacetime, exhibit several interesting yet bizarre features, which are not at all untenable for a compact stellar model of strange quark type; thus this dictates the possibility of its extra-dimensional existence. (orig.)
Spinning higher dimensional Einstein-Yang-Mills black holes
International Nuclear Information System (INIS)
Ghosh, Sushant G.; Papnoi, Uma
2014-01-01
We construct a Kerr-Newman-like spacetime starting from higher dimensional (HD) Einstein-Yang-Mills black holes via complex transformations suggested by Newman-Janis. The new metrics are a HD generalization of Kerr-Newman spacetimes which has a geometry that is precisely that of Kerr-Newman in 4D corresponding to a Yang-Mills (YM) gauge charge, but the sign of the charge term gets flipped in the HD spacetimes. It is interesting to note that the gravitational contribution of the YM gauge charge, in HD, is indeed opposite (attractive rather than repulsive) to that of the Maxwell charge. The effect of the YM gauge charge on the structure and location of static limit surface and apparent horizon is discussed. We find that static limit surfaces become less prolate with increase in dimensions and are also sensitive to the YM gauge charge, thereby affecting the shape of the ergosphere. We also analyze some thermodynamical properties of these BHs. (orig.)
Spinning higher dimensional Einstein-Yang-Mills black holes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); University of Kwa-Zulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, Private Bag 54001, Durban (South Africa); Papnoi, Uma [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India)
2014-08-15
We construct a Kerr-Newman-like spacetime starting from higher dimensional (HD) Einstein-Yang-Mills black holes via complex transformations suggested by Newman-Janis. The new metrics are a HD generalization of Kerr-Newman spacetimes which has a geometry that is precisely that of Kerr-Newman in 4D corresponding to a Yang-Mills (YM) gauge charge, but the sign of the charge term gets flipped in the HD spacetimes. It is interesting to note that the gravitational contribution of the YM gauge charge, in HD, is indeed opposite (attractive rather than repulsive) to that of the Maxwell charge. The effect of the YM gauge charge on the structure and location of static limit surface and apparent horizon is discussed. We find that static limit surfaces become less prolate with increase in dimensions and are also sensitive to the YM gauge charge, thereby affecting the shape of the ergosphere. We also analyze some thermodynamical properties of these BHs. (orig.)
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
associated 3-spaces obtained as hypersurfaces t = constant, 3-spheroids, are suit- ... pressure. Considering the Vaidya–Tikekar [12] spheroidal geometry, ... a relativistic star in hydrostatic equilibrium having the spheroidal geometry of the .... K = 1, the spheroidal 3-space degenerates into a flat 3-space and when K = 0 it.
International Nuclear Information System (INIS)
Raczka, R.
1979-01-01
Construction of non-cutoff Euclidean Green's functions for nonrenormalizable interactions Lsub(I)(phi)=lambda∫dσ(epsilon):expepsilonphi: in four-dimensional space-time is presented. It is shown that all axioms for the generating functional of E.G.F. are satisfied except perhaps the SO(4) invariance. It is shown that the singularities of E.G.F. for coinciding points are not worse than those of the free theory. (author)
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
International Nuclear Information System (INIS)
Zilhao, Miguel; Herdeiro, Carlos; Witek, Helvi; Nerozzi, Andrea; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo
2010-01-01
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
Time-dependent gravitating solitons in five dimensional warped space-times
Giovannini, Massimo
2007-01-01
Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.
A higher order space-time Galerkin scheme for time domain integral equations
Pray, Andrew J.
2014-12-01
Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method\\'s efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.
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
Higher (odd dimensional quantum Hall effect and extended dimensional hierarchy
Directory of Open Access Journals (Sweden)
Kazuki Hasebe
2017-07-01
Full Text Available We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1 monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Positioning with stationary emitters in a two-dimensional space-time
International Nuclear Information System (INIS)
Coll, Bartolome; Ferrando, Joan Josep; Morales, Juan Antonio
2006-01-01
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D 73, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make relativistic gravimetry. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coordinate system constituted by the electromagnetic signals broadcasting the proper time of the emitters are the so called emission coordinates, and we show that, in such emission coordinates, the trajectories of the emitters in both situations, the absence and presence of a gravitational field, are identical. The interesting point is that, in spite of this fact, particular additional information on the system or on the user allows us not only to distinguish both space-times, but also to complete the dynamical description of emitters and user and even to measure the mass of the gravitational field. The precise information under which these dynamical and gravimetric results may be obtained is carefully pointed out
Pair creation of higher dimensional black holes on a de Sitter background
International Nuclear Information System (INIS)
Dias, Oscar J.C.; Lemos, Jose P.S.
2004-01-01
We study in detail the quantum process in which a pair of black holes is created in a higher D-dimensional de Sitter (dS) background. The energy to materialize and accelerate the pair comes from the positive cosmological constant. The instantons that describe the process are obtained from the Tangherlini black hole solutions. Our pair creation rates reduce to the pair creation rate for Reissner-Nordstroem-dS solutions when D=4. Pair creation of black holes in the dS background becomes less suppressed when the dimension of the spacetime increases. The dS space is the only background in which we can discuss analytically the pair creation process of higher dimensional black holes, since the C-metric and the Ernst solutions, which describe, respectively, a pair accelerated by a string and by an electromagnetic field, are not known yet in a higher dimensional spacetime
Gauge fields in nonlinear group realizations involving two-dimensional space-time symmetry
International Nuclear Information System (INIS)
Machacek, M.E.; McCliment, E.R.
1975-01-01
It is shown that gauge fields may be consistently introduced into a model Lagrangian previously considered by the authors. The model is suggested by the spontaneous breaking of a Lorentz-type group into a quasiphysical two-dimensional space-time and one internal degree of freedom, loosely associated with charge. The introduction of zero-mass gauge fields makes possible the absorption via the Higgs mechanism of the Goldstone fields that appear in the model despite the fact that the Goldstone fields do not transform as scalars. Specifically, gauge invariance of the Yang-Mills type requires the introduction of two sets of massless gauge fields. The transformation properties in two-dimensional space-time suggest that one set is analogous to a charge doublet that behaves like a second-rank tensor in real four-dimensional space time. The other set suggests a spin-one-like charge triplet. Via the Higgs mechanism, the first set absorbs the Goldstone fields and acquires mass. The second set remains massless. If massive gauge fields are introduced, the associated currents are not conserved and the Higgs mechanism is no longer fully operative. The Goldstone fields are not eliminated, but coupling between the Goldstone fields and the gauge fields does shift the mass of the antisymmetric second-rank-tensor gauge field components
Neutrino stress tensor regularization in two-dimensional space-time
International Nuclear Information System (INIS)
Davies, P.C.W.; Unruh, W.G.
1977-01-01
The method of covariant point-splitting is used to regularize the stress tensor for a massless spin 1/2 (neutrino) quantum field in an arbitrary two-dimensional space-time. A thermodynamic argument is used as a consistency check. The result shows that the physical part of the stress tensor is identical with that of the massless scalar field (in the absence of Casimir-type terms) even though the formally divergent expression is equal to the negative of the scalar case. (author)
Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method
International Nuclear Information System (INIS)
Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.
2010-01-01
The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.
Higher dimensional homogeneous cosmology in Lyra geometry
Indian Academy of Sciences (India)
1Department of Mathematics, Jadavpur University, Kolkata 700 032, India. 2Khodar ... 1. Introduction. The idea of higher dimensional theory was originated in super string and super gravity .... Equation (7) can easily be integrated to obtain.
The Phase Transition of Higher Dimensional Charged Black Holes
International Nuclear Information System (INIS)
Li, Huaifan; Zhao, Ren; Zhang, Lichun; Guo, Xiongying
2016-01-01
We have studied phase transitions of higher dimensional charge black hole with spherical symmetry. We calculated the local energy and local temperature and find that these state parameters satisfy the first law of thermodynamics. We analyze the critical behavior of black hole thermodynamic system by taking state parameters (Q,Φ) of black hole thermodynamic system, in accordance with considering the state parameters (P,V) of van der Waals system, respectively. We obtain the critical point of black hole thermodynamic system and find that the critical point is independent of the dual independent variables we selected. This result for asymptotically flat space is consistent with that for AdS spacetime and is intrinsic property of black hole thermodynamic system.
Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime
Directory of Open Access Journals (Sweden)
Gianluca Calcagni
2017-10-01
Full Text Available We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.
The new Big Bang Theory according to dimensional continuous space-time theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2014-01-01
This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.
Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime
International Nuclear Information System (INIS)
Calcagni, Gianluca; Ronco, Michele
2017-01-01
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.
Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime
Calcagni, Gianluca; Ronco, Michele
2017-10-01
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.
The New Big Bang Theory according to Dimensional Continuous Space-Time Theory
Martini, Luiz Cesar
2014-04-01
This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.
A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation
Diosady, Laslo T.; Murman, Scott M.
2018-01-01
A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.
Casimir effect in a d-dimensional flat spacetime and the cut-off method
International Nuclear Information System (INIS)
Svaiter, N.F.; Svaiter, B.F.
1989-01-01
The CasiMir efeect in a D-dimensional spacetime produced by a Hermitian massless scalar field in the presence of a pair of perfectly reflecting parallel flat plates is discussed. The exponential cut-off regularization method is employed. The regularized vacuum energy and the Casimir energy of this field are evaluated and a detailed analysis of the divergent terms in the regularized vacuum energy is carried out. The two-dimensional version of the Casimir effect is discussed by means of the same cut-off method. A comparison between the above method and the zeta function regularization procedure is presented in a way which gives the unification between these two methods in the present case. (author) [pt
International Nuclear Information System (INIS)
Chen, G.S.; Christenson, J.M.
1985-01-01
In this paper, the authors present some initial results from an investigation of the application of a locally one-dimensional (LOD) finite difference method to the solution of the two-dimensional, two-group reactor kinetics equations. Although the LOD method is relatively well known, it apparently has not been previously applied to the space-time kinetics equations. In this investigation, the LOD results were benchmarked against similar computational results (using the same computing environment, the same programming structure, and the same sample problems) obtained by the TWIGL program. For all of the problems considered, the LOD method provided accurate results in one-half to one-eight of the time required by the TWIGL program
Directory of Open Access Journals (Sweden)
Haiwen Li
2018-01-01
Full Text Available The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA and direction of arrival (DOA parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM system, and the Cramer-Rao bound (CRB is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT algorithm and 2D matrix pencil (MP algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.
Execution spaces for simple higher dimensional automata
DEFF Research Database (Denmark)
Raussen, Martin
2012-01-01
Higher dimensional automata (HDA) are highly expressive models for concurrency in Computer Science, cf van Glabbeek (Theor Comput Sci 368(1–2): 168–194, 2006). For a topologist, they are attractive since they can be modeled as cubical complexes—with an inbuilt restriction for directions of allowa......Higher dimensional automata (HDA) are highly expressive models for concurrency in Computer Science, cf van Glabbeek (Theor Comput Sci 368(1–2): 168–194, 2006). For a topologist, they are attractive since they can be modeled as cubical complexes—with an inbuilt restriction for directions...
Execution spaces for simple higher dimensional automata
DEFF Research Database (Denmark)
Raussen, Martin
Higher Dimensional Automata (HDA) are highly expressive models for concurrency in Computer Science, cf van Glabbeek [26]. For a topologist, they are attractive since they can be modeled as cubical complexes - with an inbuilt restriction for directions´of allowable (d-)paths. In Raussen [25], we...
Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method
Chang, Chau-lyan
2007-01-01
The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.
Black objects and hoop conjecture in five-dimensional space-time
Energy Technology Data Exchange (ETDEWEB)
Yamada, Yuta; Shinkai, Hisa-aki, E-mail: m1m08a26@info.oit.ac.j, E-mail: shinkai@is.oit.ac.j [Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata, Osaka 573-0196 (Japan)
2010-02-21
We numerically investigated the sequences of initial data of a thin spindle and a thin ring in five-dimensional space-time in the context of the cosmic censorship conjecture. We modeled the matter in non-rotating homogeneous spheroidal or toroidal configurations under the momentarily static assumption, solved the Hamiltonian constraint equation and searched the apparent horizons. We discussed when S{sup 3} (black-hole) or S{sup 1} x S{sup 2} (black-ring) horizons ('black objects') are formed. By monitoring the location of the maximum Kretchmann invariant, an appearance of 'naked singularity' or 'naked ring' under special situations is suggested. We also discuss the validity of the hyper-hoop conjecture using a minimum area around the object, and show that the appearance of the ring horizon does not match with this hoop.
Magnetized black holes and black rings in the higher dimensional dilaton gravity
International Nuclear Information System (INIS)
Yazadjiev, Stoytcho S.
2006-01-01
In this paper we consider magnetized black holes and black rings in the higher dimensional dilaton gravity. Our study is based on exact solutions generated by applying a Harrison transformation to known asymptotically flat black hole and black ring solutions in higher dimensional spacetimes. The explicit solutions include the magnetized version of the higher dimensional Schwarzschild-Tangherlini black holes, Myers-Perry black holes, and five-dimensional (dipole) black rings. The basic physical quantities of the magnetized objects are calculated. We also discuss some properties of the solutions and their thermodynamics. The ultrarelativistic limits of the magnetized solutions are briefly discussed and an explicit example is given for the D-dimensional magnetized Schwarzschild-Tangherlini black holes
Linearized fermion-gravitation system in a (2+1)-dimensional space-time with Chern-Simons data
International Nuclear Information System (INIS)
Mello, E.R.B. de.
1990-01-01
The fermion-graviton system at linearized level in a (2+1)-dimensional space-time with the gravitational Chern-Simons term is studied. In this approximation it is shown that this system presents anomalous rotational properties and spin, in analogy with the gauge field-matter system. (A.C.A.S.) [pt
Existence of local degrees of freedom for higher dimensional pure Chern-Simons theories
International Nuclear Information System (INIS)
Banados, M.; Garay, L.J.; Henneaux, M.
1996-01-01
The canonical structure of higher dimensional pure Chern-Simons theories is analyzed. It is shown that these theories have generically a nonvanishing number of local degrees of freedom, even though they are obtained by means of a topological construction. This number of local degrees of freedom is computed as a function of the spacetime dimension and the dimension of the gauge group. copyright 1996 The American Physical Society
Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model
Energy Technology Data Exchange (ETDEWEB)
Ito, Yuta [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Graduate University for Advanced Studies (SOKENDAI),1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Tsuchiya, Asato [Department of Physics, Shizuoka University,836 Ohya, Suruga-ku, Shizuoka 422-8529 (Japan)
2017-03-27
The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing “infrared” cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power (2p) of the matrices. By performing Monte Carlo simulation of a simplified model, we find that the results become independent of p and hence universal for p≳1.3. For p as large as 2.0, however, we find that large-N scaling behaviors do not show up, and we cannot take a sensible large-N limit. Thus we find that there is a certain range of p in which a universal large-N limit can be taken. Within this range of p, the dynamical space-time dimensionality turns out to be (3+1), while for p=2.0, where we cannot take a sensible large-N limit, we observe a (5+1)d structure.
Classical testing particles and (4 + N)-dimensional theories of space-time
International Nuclear Information System (INIS)
Nieto-Garcia, J.A.
1986-01-01
The Lagrangian theory of a classical relativistic spinning test particle (top) developed by Hanson and Regge and by Hojman is briefly reviewed. Special attention is devoted to the constraints imposed on the dynamical variables associated with the system of this theory. The equations for a relativistic top are formulated in a way suitable for use in the study of geometrical properties of the 4 + N-dimensional Kaluza-Klein background. It is shown that the equations of motion of a top in five dimensions reduce to the Hanson-Regge generalization of the Bargmann-Michel-Telegdi equations of motion in four dimensions when suitable conditions on the spin tensor are imposed. The classical bosonic relativistic string theory is discussed and the connection of this theory with the top theory is examined. It is found that the relation between the string and the top leads naturally to the consideration of a 3-dimensional extended system (called terron) which sweeps out a 4-dimensional surface as it evolves in a space-time. By using a square root procedure based on ideas by Teitelboim a theory of a supersymmetric top is developed. The quantization of the new supersymmetric system is discussed. Conclusions and suggestions for further research are given
Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics
Sheykhi, Ahmad; Hashemi Asl, Doa; Dehyadegari, Amin
2018-06-01
We investigate analytically as well as numerically the properties of s-wave holographic superconductors in d-dimensional spacetime and in the presence of Logarithmic nonlinear electrodynamics. We study three aspects of this kind of superconductors. First, we obtain, by employing analytical Sturm-Liouville method as well as numerical shooting method, the relation between critical temperature and charge density, ρ, and disclose the effects of both nonlinear parameter b and the dimensions of spacetime, d, on the critical temperature Tc. We find that in each dimension, Tc /ρ 1 / (d - 2) decreases with increasing the nonlinear parameter b while it increases with increasing the dimension of spacetime for a fixed value of b. Then, we calculate the condensation value and critical exponent of the system analytically and numerically and observe that in each dimension, the dimensionless condensation get larger with increasing the nonlinear parameter b. Besides, for a fixed value of b, it increases with increasing the spacetime dimension. We confirm that the results obtained from our analytical method are in agreement with the results obtained from numerical shooting method. This fact further supports the correctness of our analytical method. Finally, we explore the holographic conductivity of this system and find out that the superconducting gap increases with increasing either the nonlinear parameter or the spacetime dimension.
Thermodynamics of higher dimensional black holes
International Nuclear Information System (INIS)
Accetta, F.S.; Gleiser, M.
1986-05-01
We discuss the thermodynamics of higher dimensional black holes with particular emphasis on a new class of spinning black holes which, due to the increased number of Casimir invariants, have additional spin degrees of freedom. In suitable limits, analytic solutions in arbitrary dimensions are presented for their temperature, entropy, and specific heat. In 5 + 1 and 9 + 1 dimensions, more general forms for these quantities are given. It is shown that the specific heat for a higher dimensional black hole is negative definite if it has only one non-zero spin parameter, regardless of the value of this parameter. We also consider equilibrium configurations with both massless particles and massive string modes. 16 refs., 3 figs
Thermodynamics of higher dimensional black holes
Energy Technology Data Exchange (ETDEWEB)
Accetta, F.S.; Gleiser, M.
1986-05-01
We discuss the thermodynamics of higher dimensional black holes with particular emphasis on a new class of spinning black holes which, due to the increased number of Casimir invariants, have additional spin degrees of freedom. In suitable limits, analytic solutions in arbitrary dimensions are presented for their temperature, entropy, and specific heat. In 5 + 1 and 9 + 1 dimensions, more general forms for these quantities are given. It is shown that the specific heat for a higher dimensional black hole is negative definite if it has only one non-zero spin parameter, regardless of the value of this parameter. We also consider equilibrium configurations with both massless particles and massive string modes. 16 refs., 3 figs.
Extended inflation from higher dimensional theories
International Nuclear Information System (INIS)
Holman, R.; Kolb, E.W.; Vadas, S.L.; Wang, Yun.
1990-04-01
The possibility is considered that higher dimensional theories may, upon reduction to four dimensions, allow extended inflation to occur. Two separate models are analayzed. One is a very simple toy model consisting of higher dimensional gravity coupled to a scalar field whose potential allows for a first-order phase transition. The other is a more sophisticated model incorporating the effects of non-trivial field configurations (monopole, Casimir, and fermion bilinear condensate effects) that yield a non-trivial potential for the radius of the internal space. It was found that extended inflation does not occur in these models. It was also found that the bubble nucleation rate in these theories is time dependent unlike the case in the original version of extended inflation
Extended inflation from higher-dimensional theories
International Nuclear Information System (INIS)
Holman, R.; Kolb, E.W.; Vadas, S.L.; Wang, Y.
1991-01-01
We consider the possibility that higher-dimensional theories may, upon reduction to four dimensions, allow extended inflation to occur. We analyze two separate models. One is a very simple toy model consisting of higher-dimensional gravity coupled to a scalar field whose potential allows for a first-order phase transition. The other is a more sophisticated model incorporating the effects of nontrivial field configurations (monopole, Casimir, and fermion bilinear condensate effects) that yield a nontrivial potential for the radius of the internal space. We find that extended inflation does not occur in these models. We also find that the bubble nucleation rate in these theories is time dependent unlike the case in the original version of extended inflation
Ahn, Junyeong; Yang, Bohm-Jung
2017-04-01
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.
Instability of higher dimensional Yang-Mills systems
International Nuclear Information System (INIS)
Randjbar-Daemi, S.; Strathdee, J.
1983-01-01
We investigate the stability of Poincare xO(3) invariant solutions for a pure semi-simple Yang-Mills, as well as Yang-Mills coupled to gravity in 6-dimensional space-time compactified over M 4 xS 2 . In contrast to the Maxwell U(1) theory (IC-82/208) in six dimensions coupled with gravity and investigated previously, the present theory exhibits tachyonic excitations and is unstable. (author)
Energy Technology Data Exchange (ETDEWEB)
Zhang, Z Y [College of Metrological Technology and Engineering, China Jiliang University, Hangzhou (China); Luo, J X [Zhejiang Radio Factory, Zhejiang (China)
2006-10-15
In order to provide a design method of the capacitive displacement transducer and to improve its measuring performance it is desperately needed to offer a refined mathematic model of the transducer of mulitiphase drive and phase-modulated. On the basis of fully considering its characteristic of digital signals, first it is found that their actual waveforms and space-time characteristics could be tersely represented by matrixes [u{sub ij}], [c{sub j}] and [v{sub i}], and corresponding matrix elements u{sub ij}, c{sub j} and v{sub i} through deeply analyzing space-time and quantum characteristics of their mulitiphase driving signals U{sub i}(t), capacitive coupling signals C{sub j}(x) and output signal V(t). and space-time transform function possessed by U(x,t) itself. Then the basic expression of the relations of the transducer is derived, which is expressed by matrixes, thereby the characteristics of space-time transform and phase modulation are brought to light. The demodulation process and demodulated waveforms and its characteristics in the transducer are also expressed by demodulated matrixes [b{sub ij}]. Finally, the reason for the principle and periodic error produced in the transducer is revealed by sampling matrix [s{sub ij}]. Thus the full process of the produce of driving signals, modulation, demodulation and space-time transform that happen in the transducer, also waveforms and characteristics of various signals in the process are concisely expressed by two-dimensional space-time matrixes. Experimental results indicate that the use of the mathematical model enables its resolving power to reach 1 {mu}m, and the mathematical model proposed is an all-things-considered model to express processes that happen in the transducer.
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
2006-01-01
In this paper we present, in a integral form, the Euclidean Green function associated with a massless scalar field in the five-dimensional Kaluza-Klein magnetic monopole superposed to a global monopole, admitting a nontrivial coupling between the field with the geometry. This Green function is expressed as the sum of two contributions: the first one related with uncharged component of the field, is similar to the Green function associated with a scalar field in a four-dimensional global monopole space-time. The second contains the information of all the other components. Using this Green function it is possible to study the vacuum polarization effects on this space-time. Explicitly we calculate the renormalized vacuum expectation value * (x)Φ(x)> Ren , which by its turn is also expressed as the sum of two contributions
Positioning in a flat two-dimensional space-time: The delay master equation
International Nuclear Information System (INIS)
Coll, Bartolome; Ferrando, Joan Josep; Morales-Lladosa, Juan Antonio
2010-01-01
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [B. Coll, J. J. Ferrando, and J. A. Morales, Phys. Rev. D 73, 084017 (2006); ibid.74, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here, generic relativistic positioning systems in the Minkowski plane are studied. The information that can be obtained from the data received by a user of the positioning system is analyzed in detail. In particular, it is shown that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so-called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. These results are illustrated with the obtention of the dynamics of the emitters and of the user from specific sets of data received by the user.
International Nuclear Information System (INIS)
Das, S.R.; Mukherji, S.
1994-01-01
We study black hole formation in a model of two dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and the constraints. We show that in the semiclassical approximation and for the generic value of a parameter which characterizes the boundary conditions, the boundary starts receding to infinity at the speed of light whenever the total energy of the incoming matter flux exceeds a certain critical value. This is also the critical energy which marks the onset of black hole formation. We then compute the quantum fluctuations of the boundary and of the rescaled scalar curvature and show that as soon as the incoming energy exceeds this critical value, and asymptotic observer using normal time resolutions will always measure large quantum fluctuations of space-time near the horizon, even though the freely falling observer does not. This is an aspect of black hole complementarity relating directly to quantum gravity effects. (author). 30 refs, 4 figs
Dimensional transition of the universe
International Nuclear Information System (INIS)
Terazawa, Hidezumi.
1989-08-01
In the extended n-dimensional Einstein theory of gravitation, where the spacetime dimension can be taken as a 'dynamical variable' which is determined by the 'Hamilton principle' of minimizing the extended Einstein-Hilbert action, it is suggested that our Universe of four-dimensional spacetime may encounter an astonishing dimensional transition into a new universe of three-dimensional or higher-than-four-dimensional spacetime. (author)
Realization of Robertson-Walker spacetimes as affine hypersurfaces
International Nuclear Information System (INIS)
Chen Bangyen
2007-01-01
Due to the growing interest in embeddings of spacetimes in higher dimensional spaces, we consider a special type of embedding. We prove that Robertson-Walker spacetimes can be embedded as centroaffine hypersurfaces and graph hypersurfaces in some affine spaces in such a way that the induced relative metrics are exactly the Lorentzian metrics on the Robertson-Walker spacetimes. Such realizations allow us to view Robertson-Walker spacetimes and their submanifolds as affine submanifolds in a natural way. Consequently, our realizations make it possible to apply the tools of affine differential geometry to study Robertson-Walker spacetimes and their submanifolds
Multifractal and higher-dimensional zeta functions
International Nuclear Information System (INIS)
Véhel, Jacques Lévy; Mendivil, Franklin
2011-01-01
In this paper, we generalize the zeta function for a fractal string (as in Lapidus and Frankenhuijsen 2006 Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (New York: Springer)) in several directions. We first modify the zeta function to be associated with a sequence of covers instead of the usual definition involving gap lengths. This modified zeta function allows us to define both a multifractal zeta function and a zeta function for higher-dimensional fractal sets. In the multifractal case, the critical exponents of the zeta function ζ(q, s) yield the usual multifractal spectrum of the measure. The presence of complex poles for ζ(q, s) indicates oscillations in the continuous partition function of the measure, and thus gives more refined information about the multifractal spectrum of a measure. In the case of a self-similar set in R n , the modified zeta function yields asymptotic information about both the 'box' counting function of the set and the n-dimensional volume of the ε-dilation of the set
Higher-dimensional black holes: hidden symmetries and separation of variables
International Nuclear Information System (INIS)
Frolov, Valeri P; Kubiznak, David
2008-01-01
In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing-Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) in 4D flat spacetime one can 'generate' the 4D Kerr-NUT-(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr-NUT-(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing-Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton-Jacobi, Klein-Gordon and Dirac equations in the general Kerr-NUT-(A)dS metrics
Stationary axisymmetric four dimensional space-time endowed with Einstein metric
International Nuclear Information System (INIS)
Hasanuddin; Azwar, A.; Gunara, B. E.
2015-01-01
In this paper, we construct Ernst equation from vacuum Einstein field equation for both zero and non-zero cosmological constant. In particular, we consider the case where the space-time admits axisymmetric using Boyer-Lindquist coordinates. This is called Kerr-Einstein solution describing a spinning black hole. Finally, we give a short discussion about the dynamics of photons on Kerr-Einstein space-time
World-volume effective theory for higher-dimensional black holes.
Emparan, Roberto; Harmark, Troels; Niarchos, Vasilis; Obers, Niels A
2009-05-15
We argue that the main feature behind novel properties of higher-dimensional black holes, compared to four-dimensional ones, is that their horizons can have two characteristic lengths of very different size. We develop a long-distance world-volume effective theory that captures the black hole dynamics at scales much larger than the short scale. In this limit the black hole is regarded as a blackfold: a black brane (possibly boosted locally) whose world volume spans a curved submanifold of the spacetime. This approach reveals black objects with novel horizon geometries and topologies more complex than the black ring, but more generally it provides a new organizing framework for the dynamics of higher-dimensional black holes.
Vacuum polarization and classical self-action near higher-dimensional defects
Energy Technology Data Exchange (ETDEWEB)
Grats, Yuri V.; Spirin, Pavel [Moscow State University, Department of Theoretical Physics, Faculty of Physics, Moscow (Russian Federation)
2017-02-15
We analyze the gravity-induced effects associated with a massless scalar field in a higher-dimensional spacetime being the tensor product of (d - n)-dimensional Minkowski space and n-dimensional spherically/cylindrically symmetric space with a solid/planar angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole (if n ≥ 3) or cosmic string (if n = 2) with (d - n - 1) flat extra dimensions. Thus, we refer to them as conical backgrounds. In terms of the angular-deficit value, we derive the perturbative expression for the scalar Green function, valid for any d ≥ 3 and 2 ≤ n ≤ d - 1, and compute it to the leading order. With the use of this Green function we compute the renormalized vacuum expectation value of the field square left angle φ{sup 2}(x) right angle {sub ren} and the renormalized vacuum averaged of the scalar-field energy-momentum tensor left angle T{sub MN}(x) right angle {sub ren} for arbitrary d and n from the interval mentioned above and arbitrary coupling constant to the curvature ξ. In particular, we revisit the computation of the vacuum polarization effects for a non-minimally coupled massless scalar field in the spacetime of a straight cosmic string. The same Green function enables to consider the old purely classical problem of the gravity-induced self-action of a classical point-like scalar or electric charge, placed at rest at some fixed point of the space under consideration. To deal with divergences, which appear in consideration of the two problems, we apply the dimensional-regularization technique, widely used in quantum field theory. The explicit dependence of the results upon the dimensionalities of both the bulk and conical submanifold is discussed. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Breban, Romulus [Institut Pasteur, Paris Cedex 15 (France)
2016-09-15
Five-dimensional (5D) space-time symmetry greatly facilitates how a 4D observer perceives the propagation of a single spinless particle in a 5D space-time. In particular, if the 5D geometry is independent of the fifth coordinate then the 5D physics may be interpreted as 4D quantum mechanics. In this work we address the case where the symmetry is approximate, focusing on the case where the 5D geometry depends weakly on the fifth coordinate. We show that concepts developed for the case of exact symmetry approximately hold when other concepts such as decaying quantum states, resonant quantum scattering, and Stokes drag are adopted, as well. We briefly comment on the optical model of the nuclear interactions and Millikan's oil drop experiment. (orig.)
International Nuclear Information System (INIS)
Hartle, J.B.
1995-01-01
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which neither require, nor always permit, a notion of state on a spacelike surface. In particular, it must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering, coarse-grained histories it may display. This spacetime notion of information coincides with the familiar one when quantum theory is formulable in terms of states on spacelike surfaces but generalizes this notion when it cannot be so formulated. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a fixed spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse grainings of sum-over-histories quantum mechanics that refer only to coordinates. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with nonunitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the ''evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics
Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods
Diosady, Laslo T.; Murman, Scott M.
2017-02-01
A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.
Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods
Diosady, Laslo T.; Murman, Scott M.
2016-01-01
space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.
Higher dimensional time-energy entanglement
International Nuclear Information System (INIS)
Richart, Daniel Lampert
2014-01-01
Judging by the compelling number of innovations based on taming quantum mechanical effects, such as the development of transistors and lasers, further research in this field promises to tackle further technological challenges in the years to come. This statement gains even more importance in the information processing scenario. Here, the growing data generation and the correspondingly higher need for more efficient computational resources and secure high bandwidth networks are central problems which need to be tackled. In this sense, the required CPU minituarization makes the design of structures at atomic levels inevitable, as foreseen by Moore's law. From these perspectives, it is necessary to concentrate further research efforts into controlling and manipulating quantum mechanical systems. This enables for example to encode quantum superposition states to tackle problems which are computationally NP hard and which therefore cannot be solved efficiently by classical computers. The only limitation affecting these solutions is the low scalability of existing quantum systems. Similarly, quantum communication schemes are devised to certify the secure transmission of quantum information, but are still limited by a low transmission bandwidth. This thesis follows the guideline defined by these research projects and aims to further increase the scalability of the quantum mechanical systems required to perform these tasks. The method used here is to encode quantum states into photons generated by spontaneous parametric down-conversion (SPDC). An intrinsic limitation of photons is that the scalability of quantum information schemes employing them is limited by the low detection efficiency of commercial single photon detectors. This is addressed by encoding higher dimensional quantum states into two photons, increasing the scalability of the scheme in comparison to multi-photon states. Further on, the encoding of quantum information into the emission-time degree of
Higher dimensional time-energy entanglement
Energy Technology Data Exchange (ETDEWEB)
Richart, Daniel Lampert
2014-07-08
Judging by the compelling number of innovations based on taming quantum mechanical effects, such as the development of transistors and lasers, further research in this field promises to tackle further technological challenges in the years to come. This statement gains even more importance in the information processing scenario. Here, the growing data generation and the correspondingly higher need for more efficient computational resources and secure high bandwidth networks are central problems which need to be tackled. In this sense, the required CPU minituarization makes the design of structures at atomic levels inevitable, as foreseen by Moore's law. From these perspectives, it is necessary to concentrate further research efforts into controlling and manipulating quantum mechanical systems. This enables for example to encode quantum superposition states to tackle problems which are computationally NP hard and which therefore cannot be solved efficiently by classical computers. The only limitation affecting these solutions is the low scalability of existing quantum systems. Similarly, quantum communication schemes are devised to certify the secure transmission of quantum information, but are still limited by a low transmission bandwidth. This thesis follows the guideline defined by these research projects and aims to further increase the scalability of the quantum mechanical systems required to perform these tasks. The method used here is to encode quantum states into photons generated by spontaneous parametric down-conversion (SPDC). An intrinsic limitation of photons is that the scalability of quantum information schemes employing them is limited by the low detection efficiency of commercial single photon detectors. This is addressed by encoding higher dimensional quantum states into two photons, increasing the scalability of the scheme in comparison to multi-photon states. Further on, the encoding of quantum information into the emission-time degree of
Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays
Energy Technology Data Exchange (ETDEWEB)
Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de [Institut für theoretische Physik, Philosophenweg 16, D-69120 Heidelberg (Germany); Noh, Changsuk, E-mail: changsuk@kias.re.kr [Korea Institute for Advanced Study, 85 Hoegiro, Seoul 130-722 (Korea, Republic of); Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com [Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 (Singapore); School of Electronic and Computer Engineering, Technical University of Crete, Chania, Crete, 73100 (Greece)
2016-11-15
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.
Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes
International Nuclear Information System (INIS)
Unver, O.; Gurtug, O.
2010-01-01
Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.
Unlabored system motion by specially conditioned electromagnetic fields in higher dimensional realms
David Froning, H.; Meholic, Gregory V.
2010-01-01
This third of three papers explores the possibility of swift, stress-less system transitions between slower-than-light and faster-than-light speeds with negligible net expenditure of system energetics. The previous papers derived a realm of higher dimensionality than 4-D spacetime that enabled such unlabored motion; and showed that fields that could propel and guide systems on unlabored paths in the higher dimensional realm must be fields that have been conditioned to SU(2) (or higher) Lie group symmetry. This paper shows that the system's surrounding vacuum dielectric ɛμ, within the higher dimensional realm's is a vector (not scalar) quantity with fixed magnitude ɛ0μ0 and changing direction within the realm with changing system speed. Thus, ɛμ generated by the system's EM field must remain tuned to vacuum ɛ0μ0 in both magnitude and direction during swift, unlabored system transitions between slower and faster than light speeds. As a result, the system's changing path and speed is such that the magnitude of the higher dimensional realm's ɛ0μ0 is not disturbed. And it is shown that a system's flight trajectories associated with its swift, unlabored transitions between zero and infinite speed can be represented by curved paths traced-out within the higher dimensional realm.
The universe as a topological defect in a higher-dimensional Einstein-Yang-Mills theory
International Nuclear Information System (INIS)
Nakamura, A.; Shiraishi, K.
1989-04-01
An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with D-dimensional EYM theory in our present analysis. A compactification leads to a D-2 dimensional effective action of Abelian gauge-Higgs theory. We find a 'vortex' solution in the effective theory. Our universe appears to be confined in a center of a 'vortex', which has D-4 large dimensions. In this paper we show an example with SU (2) symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the 'instanton-induced compactification'. The cosmological implication is also mentioned. (author)
Higher dimensional supersymmetric quantum mechanics and Dirac ...
Indian Academy of Sciences (India)
We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering `mass' as a function of coordinates. Its usefulness in solving potential problems is discussed with speciﬁc examples. We also discuss the `physical' signiﬁcance of the supersymmetric states in this formalism.
Directory of Open Access Journals (Sweden)
ShuZheng Yang
2016-01-01
Full Text Available Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordström black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi equation, we study the Hawking temperature and fermions tunneling rate at the event horizon of the higher-dimensional Reissner-Nordström black hole space-time. Finally, the correct entropy is calculation by the method beyond semiclassical approximation.
Three-dimensional gravity and Drinfel'd doubles: Spacetimes and symmetries from quantum deformations
International Nuclear Information System (INIS)
Ballesteros, Angel; Herranz, Francisco J.; Meusburger, Catherine
2010-01-01
We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra sl(2,R). We investigate the classical Drinfel'd double of a 'hybrid' deformation of sl(2,R) that depends on two parameters (η,z). With an appropriate choice of basis and real structure, this Drinfel'd double agrees with the 3d anti-de Sitter algebra. The deformation parameter η is related to the cosmological constant, while z is identified with the inverse of the speed of light and defines the signature of the metric. We generalise this result to de Sitter space, the three-sphere and 3d hyperbolic space through analytic continuation in η and z; we also investigate the limits of vanishing η and z, which yield the flat spacetimes (Minkowski and Euclidean spaces) and Newtonian models, respectively.
International Nuclear Information System (INIS)
Edelen, Dominic G B
2003-01-01
Local action of the fundamental group SO(a, 4 + k - a) is used to show that any solution of an algebraically closed differential system, that is generated from matrix Lie algebra valued 1-forms on a four-dimensional parameter space, will generate families of immersions of four-dimensional spacetimes R 4 in flat (4 + k)-dimensional spaces M 4+k with compatible signature. The algorithm is shown to work with local action of SO(a, 4 + k - a) replaced by local action of GL(4 + k). Immersions generated by local action of the Poincare group on the target spacetime are also obtained. Evaluations of the line elements, immersion loci and connection and curvature forms of these immersions are algebraic. Families of immersions that depend on one or more arbitrary functions are calculated for 1 ≤ k ≤ 4. Appropriate sections of graphs of the conformal factor for two and three interacting line singularities immersed in M 6 are given in appendix A. The local immersion theorem given in appendix B shows that all local solutions of the immersion problem are obtained by use of this method and an algebraic extension in exceptional cases
Higher-dimensional puncture initial data
International Nuclear Information System (INIS)
Zilhao, Miguel; Ansorg, Marcus; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Sperhake, Ulrich; Witek, Helvi
2011-01-01
We calculate puncture initial data, corresponding to single and binary black holes with linear momenta, which solve the constraint equations of D-dimensional vacuum gravity. The data are generated by a modification of the pseudospectral code presented in [M. Ansorg, B. Bruegmann, and W. Tichy, Phys. Rev. D 70, 064011 (2004).] and made available as the TwoPunctures thorn inside the Cactus computational toolkit. As examples, we exhibit convergence plots, the violation of the Hamiltonian constraint as well as the initial data for D=4,5,6,7. These initial data are the starting point to perform high-energy collisions of black holes in D dimensions.
New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity
Energy Technology Data Exchange (ETDEWEB)
Sundell, Per; Yin, Yihao [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago de Chile (Chile)
2017-01-11
We present new infinite-dimensional spaces of bi-axially symmetric asymptotically anti-de Sitter solutions to four-dimensional Vasiliev higher spin gravity, obtained by modifications of the Ansatz used in https://arxiv.org/abs/1107.1217, which gave rise to a Type-D solution space. The current Ansatz is based on internal semigroup algebras (without identity) generated by exponentials formed out of the bi-axial symmetry generators. After having switched on the vacuum gauge function, the resulting generalized Weyl tensor is given by a sum of generalized Petrov type-D tensors that are Kerr-like or 2-brane-like in the asymptotic AdS{sub 4} region, and the twistor space connection is smooth in twistor space over finite regions of spacetime. We provide evidence for that the linearized twistor space connection can be brought to Vasiliev gauge.
Higher dimensional generalizations of the SYK model
Energy Technology Data Exchange (ETDEWEB)
Berkooz, Micha [Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot 7610001 (Israel); Narayan, Prithvi [International Centre for Theoretical Sciences, Hesaraghatta,Bengaluru North, 560 089 (India); Rozali, Moshe [Department of Physics and Astronomy, University of British Columbia,Vancouver, BC V6T 1Z1 (Canada); Simón, Joan [School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh,King’s Buildings, Edinburgh EH9 3FD (United Kingdom)
2017-01-31
We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains N Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.
Higher dimensional uniformisation and W-geometry
International Nuclear Information System (INIS)
Govindarajan, S.
1995-01-01
We formulate the uniformisation problem underlying the geometry of W n -gravity using the differential equation approach to W-algebras. We construct W n -space (analogous to superspace in supersymmetry) as an (n-1)-dimensional complex manifold using isomonodromic deformations of linear differential equations. The W n -manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n,R) which acts properly discontinuously on a simply connected domain in bfCP n-1 . The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W-diffeomorphisms to (linear) diffeomorphisms on the W n -manifold. We discuss how the Teichmueller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the W n -manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all ''generic'' W-algebras. (orig.)
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity
International Nuclear Information System (INIS)
Zou, De-Cheng; Yue, Ruihong; Zhang, Ming
2017-01-01
We study the P-V criticality and phase transition in the extended phase space of anti-de Sitter (AdS) black holes in higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity, treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Besides the usual small/large black hole phase transitions, the interesting thermodynamic phenomena of reentrant phase transitions (RPTs) are observed for black holes in all d ≥ 6-dimensional spacetime when the coupling coefficients c_im"2 of massive potential satisfy some certain conditions. (orig.)
Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity
Energy Technology Data Exchange (ETDEWEB)
Zou, De-Cheng; Yue, Ruihong [Yangzhou University, College of Physical Science and Technology, Yangzhou (China); Zhang, Ming [Xi' an Aeronautical University, Faculty of Science, Xi' an (China)
2017-04-15
We study the P-V criticality and phase transition in the extended phase space of anti-de Sitter (AdS) black holes in higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity, treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Besides the usual small/large black hole phase transitions, the interesting thermodynamic phenomena of reentrant phase transitions (RPTs) are observed for black holes in all d ≥ 6-dimensional spacetime when the coupling coefficients c{sub i}m{sup 2} of massive potential satisfy some certain conditions. (orig.)
Pappas, T.; Kanti, P.; Pappas, N.
2016-01-01
In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de-Sitter black hole as well as on the projected-on-the-brane 4-dimensional background. The scalar fields have also a non-minimal coupling to the corresponding, bulk or brane, scalar curvature. We perform a comprehensive study by deriving exact numerical results for the greybody factors, and study their profile in terms of particle and spacetime properties. We then pro...
International Nuclear Information System (INIS)
Rami, El-Nabulsi Ahmad
2009-01-01
Higher dimensional cosmological implications of a decay law for the cosmological constant term are analyzed. Three independent cosmological models are explored mainly: 1) In the first model, the effective cosmological constant was chosen to decay with times like Δ effective = Ca -2 + D(b/a I ) 2 where a I is an arbitrary scale factor characterizing the isotropic epoch which proceeds the graceful exit period. Further, the extra-dimensional scale factor decays classically like b(t) approx. a x (t), x is a real negative number. 2) In the second model, we adopt in addition to Δ effective = Ca -2 + D(b/a I ) 2 the phenomenological law b(t) = a(t)exp( -Qt) as we expect that at the origin of time, there is no distinction between the visible and extra dimensions; Q is a real number. 3) In the third model, we study a Δ - decaying extra-dimensional cosmology with a static traversable wormhole in which the four-dimensional Friedmann-Robertson-Walker spacetime is subject to the conventional perfect fluid while the extra-dimensional part is endowed by an exotic fluid violating strong energy condition and where the cosmological constant in (3+n+1) is assumed to decays like Δ(a) = 3Ca -2 . The three models are discussed and explored in some details where many interesting points are revealed. (author)
Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?
Energy Technology Data Exchange (ETDEWEB)
Troisi, Antonio [Universita degli Studi di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Salerno (Italy)
2017-03-15
Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f(R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R) = f{sub 0}R{sup n} the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions. (orig.)
Higher dimensional global monopole in Brans–Dicke theory
Indian Academy of Sciences (India)
Keywords. Global monopole; Brans–Dicke theory; higher dimension. PACS Nos 04.20.Jb; 98.80.Bp; 04.50.+h. 1. Introduction. The idea of higher dimensional theory was originated in super string and super gravity the- ories to unify gravity with other fundamental forces in nature. Solutions of Einstein field equations in higher ...
Chen, C.-H.; Cho, H. T.; Cornell, A. S.; Harmsen, G.; Ngcobo, X.
2018-01-01
In this paper we consider spin-3 /2 fields in a D -dimensional Reissner-Nordström black hole spacetime. As these spacetimes are not Ricci flat, it is necessary to modify the covariant derivative to the supercovariant derivative, by including terms related to the background electromagnetic fields, so as to maintain the gauge symmetry. Using this supercovariant derivative we arrive at the corresponding Rarita-Schwinger equation in a charged black hole background. As in our previous works, we exploit the spherical symmetry of the spacetime and use the eigenspinor vectors on an N sphere to derive the radial equations for both nontransverse-traceless (non-TT) modes and TT modes. We then determine the quasinormal mode and absorption probabilities of the associated gauge-invariant variables using the WKB approximation and the asymptotic iteration method. We then concentrate on how these quantities change with the charge of the black hole, especially when they reach the extremal limits.
The Fuzzy analogy of chiral diffeomorphisms in higher dimensional quantum field theories
International Nuclear Information System (INIS)
Fassarella, Lucio; Schroer, Bert
2001-06-01
Our observation that the chiral diffeomorphisms allow an interpretation as modular groups of local operator algebras in the sense of Tomita and takesaki allows us to conclude that the higher deimensional generalizations are certain infinite dimensional groups which act in a 'fuzzy' way on the operator algebras of local quantum physics. These actions do not require any spacetime noncommutativity and are in complete harmony with causality and localization principles. The use of an appropriately defined isomorphism reprocesses these fuzzy actions into partially geometric actions on the holographic image and in this way tightens the relation with chiral structures and makes recent attempts to explain the required universal structure of a would be quantum Bekenstein law in terms of Virasoro algebra structures more palatable. (author)
Higher-dimensional bulk wormholes and their manifestations in brane worlds
International Nuclear Information System (INIS)
Rodrigo, Enrico
2006-01-01
There is nothing to prevent a higher-dimensional anti-de Sitter bulk spacetime from containing various other branes in addition to hosting our universe, presumed to be a positive-tension 3-brane. In particular, it could contain closed, microscopic branes that form the boundary surfaces of void bubbles and thus violate the null energy condition in the bulk. The possible existence of such micro branes can be investigated by considering the properties of the ground state of a pseudo-Wheeler-DeWitt equation describing brane quantum dynamics in minisuperspace. If they exist, a concentration of these micro branes could act as a fluid of exotic matter able to support macroscopic wormholes connecting otherwise-distant regions of the bulk. Were the brane constituting our universe to expand into a region of the bulk containing such higher-dimensional macroscopic wormholes, they would likely manifest themselves in our brane as wormholes of normal dimensionality, whose spontaneous appearance and general dynamics would seem inexplicably peculiar. This encounter could also result in the formation of baby universes of a particular type
Spacetime Junctions and the Collapse to Black Holes in Higher Dimensions
Directory of Open Access Journals (Sweden)
Filipe C. Mena
2012-01-01
Full Text Available We review recent results about the modelling of gravitational collapse to black holes in higher dimensions. The models are constructed through the junction of two exact solutions of the Einstein field equations: an interior collapsing fluid solution and a vacuum exterior solution. The vacuum exterior solutions are either static or containing gravitational waves. We then review the global geometrical properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. In the case of radiating exteriors, we show that the data at the boundary can be chosen to be, in some sense, arbitrarily close to the data for the Schwarzschild-Tangherlini solution.
CFT description of three-dimensional Kerr-de Sitter spacetime
International Nuclear Information System (INIS)
Fjelstad, Jens; Hwang, Stephen; Maansson, Teresia
2002-01-01
We describe three-dimensional Kerr-de Sitter space using similar methods as recently applied to the BTZ black hole. A rigorous form of the classical connection between gravity in three dimensions and two-dimensional conformal field theory is employed, where the fundamental degrees of freedom are described in terms of two dependent SL(2,C) currents. In contrast to the BTZ case, however, quantization does not give the Bekenstein-Hawking entropy connected to the cosmological horizon of Kerr-de Sitter space
CFT description of three-dimensional Kerr-de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Fjelstad, Jens E-mail: jens.fjelstad@kau.se; Hwang, Stephen E-mail: stephen.hwang@kau.se; Maansson, Teresia E-mail: teresia@physto.se
2002-10-07
We describe three-dimensional Kerr-de Sitter space using similar methods as recently applied to the BTZ black hole. A rigorous form of the classical connection between gravity in three dimensions and two-dimensional conformal field theory is employed, where the fundamental degrees of freedom are described in terms of two dependent SL(2,C) currents. In contrast to the BTZ case, however, quantization does not give the Bekenstein-Hawking entropy connected to the cosmological horizon of Kerr-de Sitter space.
Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time
Energy Technology Data Exchange (ETDEWEB)
Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)
2014-11-15
This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)
International Nuclear Information System (INIS)
Aoyama, Tatsumi; Kawai, Hikaru; Shibusa, Yuuichiro
2006-01-01
We investigate the origin of our four-dimensional space-time by considering dynamical aspects of the IIB matrix model using the improved mean field approximation. Previous works have focused on the specific choices of configurations as ansatz which preserve SO(d) rotational symmetry. In this report, an extended ansatz is proposed and examined up to a third-order approximation which includes both the SO(4) ansatz and the SO(7) ansatz in their respective limits. From the solutions of the self-consistency condition represented by the extrema of the free energy of the system, it is found that some of the solutions found in the SO(4) or SO(7) ansatz disappear in the extended ansatz. This implies that the extension of ansatz can be used to distinguish stable solutions from unstable solutions. It is also found that there is a non-trivial accumulation of extrema including the SO(4)-preserving solution, which may lead to the formation of a plateau. (author)
Virasoro algebra with central charge c=1 on the horizon of a two-dimensional-Rindler space-time
International Nuclear Information System (INIS)
Moretti, Valter; Pinamonti, Nicola
2004-01-01
Using the holographic machinery built up in a previous work, we show that the hidden SL(2,R) symmetry of a scalar quantum field propagating in a Rindler space-time admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra defined in the Fock representation. That representation has central charge c=1. The Virasoro algebra of operators gets a manifest geometrical meaning if referring to the holographically associated quantum field theory on the horizon: It is nothing but a representation of the algebra of vector fields defined on the horizon equipped with a point at infinity. All that happens provided the Virasoro ground energy hcoloneμ 2 /2 vanishes and, in that case, the Rindler Hamiltonian is associated with a certain Virasoro generator. If a suitable regularization procedure is employed, for h=1/2, the ground state of that generator seems to correspond to a thermal state when examined in the Rindler wedge, taking the expectation value with respect to Rindler time. Finally, under Wick rotation in Rindler time, the pair of quantum field theories which are built up on the future and past horizon defines a proper two-dimensional conformal quantum field theory on a cylinder
International Nuclear Information System (INIS)
Baig, M.; Colet, J.
1986-01-01
Using Monte Carlo simulations the SU(2)xU(1) lattice gauge theory has been analyzed, which is equivalent for the Wilson action to a U(2) theory, at space-time dimensionalities from d=3 to 5. It has been shown that there exist first-order phase transitions for both d=4 and d=5. A monopole-condensation mechanism seems to be responsible for these phase transitions. At d=3 no phase transitions have been detected. (orig.)
International Nuclear Information System (INIS)
Sokolov, S.N.; Tret'yak, V.I.
1985-01-01
The Lagrangian relativistic theory in the two-dimensional space-time in the front form of dynamics is formulated and its connections with the predictive mechanics, with the Hamiltonian description, and with the Fokker-type action theory are established. The relations are found in a closed form without using formal expansions. The existence of mathematical limitations on a magnitude of Lagrangians of two-particle interactions is shown
Fermion emission in a two-dimensional black hole space-time
International Nuclear Information System (INIS)
Wanders, G.
1994-01-01
We investigate massless fermion production by a two-dimensional dilatonic black hole. Our analysis is based on the Bogoliubov transformation relating the outgoing fermion field observed outside the black hole horizon to the incoming field present before the black hole creation. It takes full account of the fact that the transformation is neither invertible nor unitarily implementable. The particle content of the outgoing radiation is specified by means of inclusive probabilities for the detection of sets of outgoing fermions and antifermions in given states. For states localized near the horizon these probabilities characterize a thermal equilibrium state. The way the probabilities become thermal as one approaches the horizon is discussed in detail
Static wormhole solution for higher-dimensional gravity in vacuum
International Nuclear Information System (INIS)
Dotti, Gustavo; Oliva, Julio; Troncoso, Ricardo
2007-01-01
A static wormhole solution for gravity in vacuum is found for odd dimensions greater than four. In five dimensions the gravitational theory considered is described by the Einstein-Gauss-Bonnet action where the coupling of the quadratic term is fixed in terms of the cosmological constant. In higher dimensions d=2n+1, the theory corresponds to a particular case of the Lovelock action containing higher powers of the curvature, so that in general, it can be written as a Chern-Simons form for the AdS group. The wormhole connects two asymptotically locally AdS spacetimes each with a geometry at the boundary locally given by RxS 1 xH d-3 . Gravity pulls towards a fixed hypersurface located at some arbitrary proper distance parallel to the neck. The causal structure shows that both asymptotic regions are connected by light signals in a finite time. The Euclidean continuation of the wormhole is smooth independently of the Euclidean time period, and it can be seen as instanton with vanishing Euclidean action. The mass can also be obtained from a surface integral and it is shown to vanish
Massive quantum field theory in two-dimensional Robertson-Walker space-time
International Nuclear Information System (INIS)
Bunch, T.S.; Christensen, S.M.; Fulling, S.A.
1978-01-01
The stress tensor of a massive scalar field, as an integral over normal modes (which are not mere plane waves), is regularized by covariant point separation. When the expectation value in a Parker-Fulling adiabatic vacuum state is expanded in the limit of small curvature-to-mass ratios, the series coincides in each order with the Schwinger-DeWitt-Christensen proper-time expansion. The renormalization ansatz suggested by these expansions (which applies to arbitrary curvature-to-mass ratios and arbitrary quantum state) can be implemented at the integrand level for practical computations. The renormalized tensor (1) passes in the massless limit, for appropriate choice of state, to the known vacuum stress of a massless field, (2) agrees with the explicit results of Bernard and Duncan for a special model, and (3) has a nonzero vacuum expectation value in the two-dimensional ''Milne universe'' (flat space in hyperbolic coordinates). Following Wald, we prove that the renormalized tensor is conserved and point out that there is no arbitrariness in the renormalization procedure. The general approach of this paper is applicable to four-dimensional models
Space-time topology optimization for one-dimensional wave propagation
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2009-01-01
-dimensional transient wave propagation in an elastic rod with time dependent Young's modulus. By two simulation examples it is demonstrated how dynamic structures can display rich dynamic behavior such as wavenumber/frequency shifts and lack of energy conservation. The optimization method's potential for creating...... structures with novel dynamic behavior is illustrated by a simple example; it is shown that an elastic rod in which the optimized stiffness distribution is allowed to vary in time can be much more efficient in prohibiting wave propagation compared to a static bandgap structure. Optimized designs in form...... of spatio-temporal laminates and checkerboards are generated and discussed. The example lays the foundation for creating designs with more advanced functionalities in future work....
Higher Dimensional Kerr-Schild Spacetimes with (A)dS Background
Czech Academy of Sciences Publication Activity Database
Málek, T.; Pravda, Vojtěch
2011-01-01
Roč. 314, - (2011), 012111 ISSN 1742-6588. [Spanish Relativity Meeting (ERE 2010). Granada, 06.09.2010-10.09.2010] R&D Projects: GA ČR GAP203/10/0749 Institutional research plan: CEZ:AV0Z10190503 Keywords : Kerr-Schild metrics * Einstein equations Subject RIV: BA - General Mathematics http://iopscience.iop.org/1742-6596/314/1/012111
On conformal Paneitz curvature equations in higher dimensional spheres
International Nuclear Information System (INIS)
El Mehdi, Khalil
2004-11-01
We study the problem of prescribing the Paneitz curvature on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of such critical points at infinity, we prove some existence results. (author)
Scalar QNMs for higher dimensional black holes surrounded by quintessence in Rastall gravity
Energy Technology Data Exchange (ETDEWEB)
Graca, J.P.M.; Lobo, Iarley P. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil)
2018-02-15
The spacetime solution for a black hole, surrounded by an exotic matter field, in Rastall gravity, is calculated in an arbitrary d-dimensional spacetime. After this, we calculate the scalar quasinormal modes of such solution, and study the shift on the modes caused by the modification of the theory of gravity, i.e., by the introduction of a new term due to Rastall. We conclude that the shift strongly depends on the kind of exotic field one is studying, but for a low density matter that supposedly pervades the universe, it is unlikely that Rastall gravity will cause an instability for the probe field. (orig.)
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)
Black holes in higher dimensional gravity theory with corrections quadratic in curvature
International Nuclear Information System (INIS)
Frolov, Valeri P.; Shapiro, Ilya L.
2009-01-01
Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form C 2 =C αβγδ C αβγδ . The Gauss-Bonnet equation in four-dimensional spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar C 2 correction. An important new feature of the spaces with dimension D>4 is that in the presence of the Weyl curvature-squared term a necessary solution differs from the corresponding 'classical' vacuum Tangherlini metric. This difference is related to the presence of secondary or induced hair. We explore how the Tangherlini solution is modified by 'quantum corrections', assuming that the gravitational radius r 0 is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ordinary differential equation (master equation).
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Higher-Dimensional Solitons Stabilized by Opposite Charge
Binder, B
2002-01-01
In this paper it is shown how higher-dimensional solitons can be stabilized by a topological phase gradient, a field-induced shift in effective dimensionality. As a prototype, two instable 2-dimensional radial symmetric Sine-Gordon extensions (pulsons) are coupled by a sink/source term such, that one becomes a stable 1d and the other a 3d wave equation. The corresponding physical process is identified as a polarization that fits perfectly to preliminary considerations regarding the nature of electric charge and background of 1/137. The coupling is iterative with convergence limit and bifurcation at high charge. It is driven by the topological phase gradient or non-local Gauge potential that can be mapped to a local oscillator potential under PSL(2,R).
Diffusion in higher dimensional SYK model with complex fermions
Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong
2018-01-01
We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.
Higher-dimensional analogues of Donaldson-Witten theory
International Nuclear Information System (INIS)
Acharya, B.S.; Spence, B.
1997-01-01
We present a Donaldson-Witten-type field theory in eight dimensions on manifolds with Spin(7) holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi-Yau threefolds and manifolds of G 2 holonomy, respectively. We point out that these theories arise by considering supersymmetric Yang-Mills theory defined on such manifolds. The theories are invariant under metric variations preserving the holonomy structure without the need for twisting. This statement is a higher-dimensional analogue of the fact that Donaldson-Witten field theory on hyper-Kaehler 4-manifolds is topological without twisting. Higher-dimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory. (orig.)
The Peierls argument for higher dimensional Ising models
International Nuclear Information System (INIS)
Bonati, Claudio
2014-01-01
The Peierls argument is a mathematically rigorous and intuitive method to show the presence of a non-vanishing spontaneous magnetization in some lattice models. This argument is typically explained for the D = 2 Ising model in a way which cannot be easily generalized to higher dimensions. The aim of this paper is to present an elementary discussion of the Peierls argument for the general D-dimensional Ising model. (paper)
Higher dimensional strange quark matter solutions in self creation cosmology
Energy Technology Data Exchange (ETDEWEB)
Şen, R., E-mail: ramazansen-1991@hotmail.com [Institute for Natural and Applied Sciences, Çanakkale Onsekiz Mart University, 17020, Çanakkale (Turkey); Aygün, S., E-mail: saygun@comu.edu.tr [Department of Physics, Art and Science Faculty, Çanakkale Onsekiz Mart University, Çanakkale 17020 (Turkey)
2016-03-25
In this study, we have generalized the higher dimensional flat Friedmann-Robertson-Walker (FRW) universe solutions for a cloud of string with perfect fluid attached strange quark matter (SQM) in Self Creation Cosmology (SCC). We have obtained that the cloud of string with perfect fluid does not survive and the string tension density vanishes for this model. However, we get dark energy model for strange quark matter with positive density and negative pressure in self creation cosmology.
Bisimulation for Higher-Dimensional Automata. A Geometric Interpretation
DEFF Research Database (Denmark)
Fahrenberg, Ulrich
We show how parallel compostition of higher-dimensional automata (HDA) can be expressed categorically in the spirit of Winskel & Nielsen. Employing the notion of computation path introduced by van Glabbeek, we define a new notion of bisimulation of HDA using open maps. We derive a connection...... between computation paths and carrier sequences of dipaths and show that bisimilarity of HDA can be decided by the use of geometric techniques....
Accretion onto a charged higher-dimensional black hole
International Nuclear Information System (INIS)
Sharif, M.; Iftikhar, Sehrish
2016-01-01
This paper deals with the steady-state polytropic fluid accretion onto a higher-dimensional Reissner-Nordstroem black hole. We formulate the generalized mass flux conservation equation, energy flux conservation and relativistic Bernoulli equation to discuss the accretion process. The critical accretion is investigated by finding the critical radius, the critical sound velocity, and the critical flow velocity. We also explore gas compression and temperature profiles to analyze the asymptotic behavior. It is found that the results for the Schwarzschild black hole are recovered when q = 0 in four dimensions. We conclude that the accretion process in higher dimensions becomes slower in the presence of charge. (orig.)
Accretion onto a charged higher-dimensional black hole
Energy Technology Data Exchange (ETDEWEB)
Sharif, M.; Iftikhar, Sehrish [University of the Punjab, Department of Mathematics, Lahore (Pakistan)
2016-03-15
This paper deals with the steady-state polytropic fluid accretion onto a higher-dimensional Reissner-Nordstroem black hole. We formulate the generalized mass flux conservation equation, energy flux conservation and relativistic Bernoulli equation to discuss the accretion process. The critical accretion is investigated by finding the critical radius, the critical sound velocity, and the critical flow velocity. We also explore gas compression and temperature profiles to analyze the asymptotic behavior. It is found that the results for the Schwarzschild black hole are recovered when q = 0 in four dimensions. We conclude that the accretion process in higher dimensions becomes slower in the presence of charge. (orig.)
Bianchi's Bäcklund transformation for higher dimensional quadrics
Dincă, Ion I.
2016-12-01
We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics (which is also a generalization of Tenenblat-Terng's Bäcklund transformation of isometric deformations of Hn(R) in R 2 n - 1 to general quadrics). Our investigation is the higher dimensional version of Bianchi's main three theorems on the theory of isometric deformations of quadrics and Bianchi's treatment of the Bäcklund transformation for diagonal paraboloids via conjugate systems. It became the driving force which led to the flourishing of the classical differential geometry in the second half of the XIX th century and its profound study by illustrious geometers led to interesting results. Today it is still an open problem in its full generality, but basic familiar results like the Gauß-Bonnet fundamental theorem of surfaces and the Codazzi-Mainardi equations (independently discovered also by Peterson) were first communicated to the French Academy of Sciences. A list (most likely incomplete) of the winners of the prize includes Bianchi, Bonnet, Guichard, Weingarten.Up to 1899 isometric deformations of the (pseudo-)sphere and isotropic quadrics without center (from a metric point of view they can be considered as metrically degenerate quadrics without center) together with their Bäcklund transformation and the complementary transformation of isometric deformations of surfaces of revolution were investigated by geometers such as Bäcklund, Bianchi, Bonnet, Darboux, Goursat, Hazzidakis, Lie, Weingarten, etc.In 1899 Guichard discovered that when quadrics with(out) center and of revolution around the focal axis roll on their isometric deformations their foci describe constant mean curvature (minimal) surfaces (and Bianchi proved the converse: all constant mean curvature (minimal) surfaces can be realized in this way).With Guichard's result the race to find the isometric deformations of general quadrics was on; it ended with Bianchi
Higher dimensional curved domain walls on Kähler surfaces
Energy Technology Data Exchange (ETDEWEB)
Akbar, Fiki T., E-mail: ftakbar@fi.itb.ac.id [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no. 10 Bandung, 40132 (Indonesia); Gunara, Bobby E., E-mail: bobby@fi.itb.ac.id [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no. 10 Bandung, 40132 (Indonesia); Radjabaycolle, Flinn C. [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no. 10 Bandung, 40132 (Indonesia); Departement of Physics, Faculty of Mathematics and Natural Sciences, Cendrawasih University, Jl. Kampwolker Kampus Uncen Baru Waena-Jayapura 99351 (Indonesia); Wijaya, Rio N. [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no. 10 Bandung, 40132 (Indonesia)
2017-03-15
In this paper we study some aspects of curved BPS-like domain walls in higher dimensional gravity theory coupled to scalars where the scalars span a complex Kähler surface with scalar potential turned on. Assuming that a fake superpotential has a special form which depends on Kähler potential and a holomorphic function, we prove that BPS-like equations have a local unique solution. Then, we analyze the vacuum structure of the theory including their stability using dynamical system and their existence in ultraviolet-infrared regions using renormalization group flow.
Ultraviolet divergences in higher dimensional supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Howe, P.S.; Stelle, K.S.
1984-01-01
We determine the loop orders for the onset of allowed ultra-violet divergences in higher dimensional supersymmetric Yang-Mills theories. Cancellations are controlled by the non-renormalization theorems for the linearly realizable supersymmetries and by the requirement that counterterms display the full non-linear supersymmetries when the classical equations of motion are imposed. The first allowed divergences in the maximal super Yang-Mills theories occur at four loops in five dimensions, three loops in six dimensions and two loops in seven dimensions. (orig.)
Higher dimensional curved domain walls on Kähler surfaces
International Nuclear Information System (INIS)
Akbar, Fiki T.; Gunara, Bobby E.; Radjabaycolle, Flinn C.; Wijaya, Rio N.
2017-01-01
In this paper we study some aspects of curved BPS-like domain walls in higher dimensional gravity theory coupled to scalars where the scalars span a complex Kähler surface with scalar potential turned on. Assuming that a fake superpotential has a special form which depends on Kähler potential and a holomorphic function, we prove that BPS-like equations have a local unique solution. Then, we analyze the vacuum structure of the theory including their stability using dynamical system and their existence in ultraviolet-infrared regions using renormalization group flow.
Exact coefficients for higher dimensional operators with sixteen supersymmetries
Energy Technology Data Exchange (ETDEWEB)
Chen, Wei-Ming [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); Huang, Yu-tin [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Wen, Congkao [INFN Sezione di Roma “Tor Vergata' ,Via della Ricerca Scientifica, 00133 Roma (Italy)
2015-09-15
We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F{sup n} with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F{sup 4}. As the F{sup 4} coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficients are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.
International Nuclear Information System (INIS)
Doplicher, S.
1996-01-01
We review some recent result and work in progress on the quantum structure of spacetime at scales comparable with the Planck length; the models discussed here are operationally motivated by the limitations in the accuracy of localization of events in spacetime imposed by the interplay between quantum mechanics and classical general relativity. (orig.)
The extensions of space-time. Physics in the 8-dimensional homogeneous space D = SU(2,2)/K
International Nuclear Information System (INIS)
Barut, A.O.
1993-07-01
The Minkowski space-time is only a boundary of a bigger homogeneous space of the conformal group. The conformal group is the symmetry group of our most fundamental massless wave equations. These extended groups and spaces have many remarkable properties and physical implications. (author). 36 refs
Kanti, P.; Pappas, T.
2017-07-01
The absence of a true thermodynamical equilibrium for an observer located in the causal area of a Schwarzschild-de Sitter spacetime has repeatedly raised the question of the correct definition of its temperature. In this work, we consider five different temperatures for a higher-dimensional Schwarzschild-de Sitter black hole: the bare T0, the normalized TBH, and three effective ones given in terms of both the black-hole and cosmological horizon temperatures. We find that these five temperatures exhibit similarities but also significant differences in their behavior as the number of extra dimensions and the value of the cosmological constant are varied. We then investigate their effect on the energy emission spectra of Hawking radiation. We demonstrate that the radiation spectra for the normalized temperature TBH—proposed by Bousso and Hawking over twenty years ago—leads to the dominant emission curve, while the other temperatures either support a significant emission rate only in a specific Λ regime or have their emission rates globally suppressed. Finally, we compute the bulk-over-brane emissivity ratio and show that the use of different temperatures may lead to different conclusions regarding the brane or bulk dominance.
Ambient cosmology and spacetime singularities
International Nuclear Information System (INIS)
Antoniadis, Ignatios; Cotsakis, Spiros
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
Graviton emission from a higher-dimensional black hole
International Nuclear Information System (INIS)
Cornell, Alan S.; Naylor, Wade; Sasaki, Misao
2006-01-01
We discuss the graviton absorption probability (greybody factor) and the cross-section of a higher-dimensional Schwarzschild black hole (BH). We are motivated by the suggestion that a great many BHs may be produced at the LHC and bearing this fact in mind, for simplicity, we shall investigate the intermediate energy regime for a static Schwarzschild BH. That is, for (2M) 1/(n-1) ω ∼ 1, where M is the mass of the black hole and ω is the energy of the emitted gravitons in (2+n)-dimensions. To find easily tractable solutions we work in the limit l >> 1, where l is the angular momentum quantum number of the graviton
The dynamical structure of higher dimensional Chern-Simons theory
International Nuclear Information System (INIS)
Banados, M.; Garay, L.J.; Henneaux, M.
1996-01-01
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry out the complete Dirac Hamiltonian analysis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G x U(1). We also study the algebra of surface charges that arise in the presence of boundaries and show that it is isomorphic to the WZW 4 discussed in the literature. Some applications are then considered. It is shown, in particular, that Chern-Simons gravity in dimensions greater than or equal to five has a propagating torsion. (orig.)
Pappas, T.; Kanti, P.; Pappas, N.
2016-07-01
In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de Sitter black hole as well as on the projected-on-the-brane four-dimensional background. The scalar fields have also a nonminimal coupling to the corresponding, bulk or brane, scalar curvature. We perform a comprehensive study by deriving exact numerical results for the greybody factors, and study their profile in terms of particle and spacetime properties. We then proceed to derive the Hawking radiation spectra for a higher-dimensional Schwarzschild-de Sitter black hole, and we study both bulk and brane channels. We demonstrate that the nonminimal field coupling, which creates an effective mass term for the fields, suppresses the energy emission rates while the cosmological constant assumes a dual role. By computing the relative energy rates and the total emissivity ratio for bulk and brane emission, we demonstrate that the combined effect of a large number of extra dimensions and value of the field coupling gives to the bulk channel the clear domination in the bulk-brane energy balance.
Space-Time Crystal and Space-Time Group.
Xu, Shenglong; Wu, Congjun
2018-03-02
Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1+1D) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D+1)-dimensional space-time crystal.
The signature triality of Majorana-Weyl spacetimes
International Nuclear Information System (INIS)
Andrade, M.A. de; Rojas, M.; Toppan, F.
2000-05-01
The Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin (8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's superstrings, five-branes, F-theory, are shown to be interconnected via the S 3 permutation group. Bilinear and trilinear invariants under spacetime triality are introduced and their possible relevance in building models possessing a space-versus-time exchange symmetry is discussed. Moreover the Cartan's vector/chiral spinor/antichiral spinor triality of SO (8) and SO(4,4) is analyzed in detail and explicit formulas are produced in a Majorana-Weyl basis. This paper is the extended version of hep-th/9907148. (author)
The Higgs particle and higher-dimensional theories
International Nuclear Information System (INIS)
Lim, C. S.
2014-01-01
In spite of the great success of LHC experiments, we do not know whether the discovered “standard model-like” Higgs particle is really what the standard model predicts, or a particle that some new physics has in its low-energy effective theory. Also, the long-standing problems concerning the property of the Higgs and its interactions are still there, and we still do not have any conclusive argument on the origin of the Higgs itself. In this article we focus on higher-dimensional theories as new physics. First we give a brief review of their representative scenarios and closely related 4D scenarios. Among them, we mainly discuss two interesting possibilities of the origin of the Higgs: the Higgs as a gauge boson and the Higgs as a (pseudo) Nambu–Goldstone boson. Next, we argue that theories of new physics are divided into two categories, i.e., theories with normal Higgs interactions and those with anomalous Higgs interactions. Interestingly, both the candidates for the origin of the Higgs mentioned above predict characteristic “anomalous” Higgs interactions, such as the deviation of the Yukawa couplings from the standard model predictions. Such deviations can hopefully be investigated by precision tests of Higgs interactions at the planned ILC experiment. Also discussed is the main decay mode of the Higgs, H→γγ. Again, theories belonging to different categories are known to predict remarkably different new physics contributions to this important process
Massive Higher Dimensional Gauge Fields as Messengers of Supersymmetry Breaking
International Nuclear Information System (INIS)
Chacko, Z.; Luty, Markus A.; Ponton, Eduardo
2000-01-01
We consider theories with one or more compact dimensions with size r > 1/M, where M is the fundamental Planck scale, with the visible and hidden sectors localized on spatially separated 3 -branes''. We show that a bulk U(1) gauge field spontaneously broken on the hidden-sector 3-brane is an attractive candidate for the messenger of supersymmetry breaking. In this scenario scalar mass-squared terms are proportional to U(1) charges, and therefore naturally conserve flavor. Arbitrary flavor violation at the Planck scale gives rise to exponentially suppressed flavor violation at low energies. Gaugino masses can be generated if the standard gauge fields propagate in the bulk; μ and Bμ terms can be generated by the Giudice-Masiero or by the VEV of a singlet in the visible sector. The latter case naturally solves the SUSY CP problem. Realistic phenomenology can be obtained either if all microscopic parameters are order one in units of M, or if the theory is strongly coupled at the scale M. (For the latter case, we estimate parameters by extending n aive dimensional analysis'' to higher-dimension theories with branes.) In either case, the only unexplained hierarchy is the l arge'' size of the extra dimensions in fundamental units, which need only be an order of magnitude. All soft masses are naturally within an order of magnitude of m 3/2 , and trilinear scalar couplings are negligible. Squark and slepton masses can naturally unify even in the absence of grand unification. (author)
An approach to higher dimensional theories based on lattice gauge theory
International Nuclear Information System (INIS)
Murata, M.; So, H.
2004-01-01
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram
z -Weyl gravity in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Moon, Taeyoon; Oh, Phillial, E-mail: dpproject@skku.edu, E-mail: ploh@skku.edu [Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of)
2017-09-01
We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the foliation preserving diffeomorphism invariance adapted to the extra dimensions, thus keeping the general covariance only for the four dimensional spacetime. The conformally invariant gravity can be constructed with an extra (Weyl) scalar field and a real parameter z which describes the degree of anisotropy of conformal transformation between the spacetime and extra dimensional metrics. In the zero mode effective 4D action, it reduces to four-dimensional scalar-tensor theory coupled with nonlinear sigma model described by extra dimensional metrics. There are no restrictions on the value of z at the classical level and possible applications to the cosmological constant problem with a specific choice of z are discussed.
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)
Euclidean D-branes and higher-dimensional gauge theory
International Nuclear Information System (INIS)
Acharya, B.S.; Figueroa-O'Farrill, J.M.; Spence, B.; O'Loughlin, M.
1997-07-01
We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane-that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory-is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N T =2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G 2 holonomy. (author). 22 refs, 3 tabs
International Nuclear Information System (INIS)
Silva O, G.; Garcia G, P.
2004-01-01
In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three dimensional Minkowski metric. (Author)
Higher-dimensional cosmological model with variable gravitational ...
Indian Academy of Sciences (India)
We have studied five-dimensional homogeneous cosmological models with variable and bulk viscosity in Lyra geometry. Exact solutions for the field equations have been obtained and physical properties of the models are discussed. It has been observed that the results of new models are well within the observational ...
International Nuclear Information System (INIS)
Aboanber, A.E.; Hamada, Y.M.
2008-01-01
An extensive knowledge of the spatial power distribution is required for the design and analysis of different types of current-generation reactors, and that requires the development of more sophisticated theoretical methods. Therefore, the need to develop new methods for multidimensional transient reactor analysis still exists. The objective of this paper is to develop a computationally efficient numerical method for solving the multigroup, multidimensional, static and transient neutron diffusion kinetics equations. A generalized Runge-Kutta method has been developed for the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic time step control. In addition, the A(α)-stability properties of the method are investigated. The analyses of two- and three-dimensional benchmark problems as well as static and transient problems, demonstrate that very accurate solutions can be obtained with assembly-sized spatial meshes. Preliminary numerical evaluations using two- and three-dimensional finite difference codes showed that the presented generalized Runge-Kutta method is highly accurate and efficient when compared with other optimized iterative numerical and conventional finite difference methods
Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols
Directory of Open Access Journals (Sweden)
Simon J. Gay
2014-07-01
Full Text Available We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. We have extended the quantum process calculus to describe d-dimensional quantum systems, which has not been done before. We summarise the necessary theory in the generalisation of quantum gates and Bell states and use the theory to apply the quantum process calculus CQP to quantum protocols, namely qudit teleportation and superdense coding.
Ohanian, Hans C
2013-01-01
The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with chapters on cosmology an...
Unitarity in three-dimensional flat space higher spin theories
International Nuclear Information System (INIS)
Grumiller, D.; Riegler, M.; Rosseel, J.
2014-01-01
We investigate generic flat-space higher spin theories in three dimensions and find a no-go result, given certain assumptions that we spell out. Namely, it is only possible to have at most two out of the following three properties: unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity provides an (algebra-dependent) upper bound on the central charge, like c=42 for the Galilean W_4"("2"−"1"−"1") algebra. We extend this no-go result to rule out unitary “multi-graviton” theories in flat space. We also provide an example circumventing the no-go result: Vasiliev-type flat space higher spin theory based on hs(1) can be unitary and simultaneously allow for non-trivial higher-spin states in the dual field theory.
Two-dimensional N=(2,2) lattice gauge theories with matter in higher representations
International Nuclear Information System (INIS)
Joseph, Anosh
2014-06-01
We construct two-dimensional N=(2,2) supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU(N c ) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gauge-invariant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.
International Nuclear Information System (INIS)
Ezaki, Masahiro; Mitake, Susumu; Ozawa, Tamotsu
1979-06-01
The SCOTCH program solves the one-dimensional (R or Z), two-group reactor kinetics equations with multi-channel temperature transients and fluid dynamics. Sub-program SCOTCH-RX simulates the space-time neutron diffusion in radial direction, and sub-program SCOTCH-AX simulates the same in axial direction. The program has about 8,000 steps of FORTRAN statement and requires about 102 kilo-words of computer memory. (author)
Energy Technology Data Exchange (ETDEWEB)
Ferroukhi, H.; Coddington, P
2001-03-01
One of the activities within the STARS project, in the Laboratory for Reactor Physics and System Behaviour; is the development of a coupling methodology between the three-dimensional, space-time kinetics codes CORETRAN and RETRAN-3D in order to perform core and plant transient analyses of the Swiss LWRs. The CORETRAN code is a 3-D full-core simulator, intended to be used for core-related analyses, while RETRAN-3D is the three-dimensional kinetics version of the plant system code RETRAN, and can therefore be used for best-estimate analyses of a wide range of transients in both PWRs and BWRs. Because the neutronics solver in both codes is based on the same kinetics model, one important advantage is that the codes can be coupled so that the initial conditions for a RETRAN-3D plant analysis are generated by a detailed-core, steady-state calculation using CORETRAN. As a first step towards using CORETRAN and RETRAN-3D for kinetic applications, the NEACRP PWR rod ejection benchmark has been analyzed with both codes, and is presented in this paper. The first objective is to verify the consistency between the static and kinetic solutions of the two codes, and so gain confidence in the coupling methodology. The second objective is to assess the CORETRAN and RETRAN-3D solutions for a well-defined RIA transient, comparing with previously published results. In parallel, several sensitivity studies have been performed in an attempt to identify models and calculational options important for a correct analysis of an RIA event in a LWR using these two codes. (author)
Gravitational collapse in higher-dimensional charged-Vaidya space ...
Indian Academy of Sciences (India)
time. We show that singularities arising in a charged null fluid in higher dimension are always naked violating ... of matter is one of the most active field of research in the contemporary general relativity. ... The main open issue ..... [3] A Papapetrou, in A random walk in relativity and cosmology edited by N Dadhich, J K Rao,.
Quantum gravity effects in Myers-Perry space-times
International Nuclear Information System (INIS)
Litim, Daniel F.; Nikolakopoulos, Konstantinos
2014-01-01
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton’s coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions
Casimir energy and the possibility of higher dimensional manipulation
Obousy, R. K.; Saharian, A. A.
2009-01-01
It is well known that the Casimir effect is an excellent candidate for the stabilization of the extra dimensions. It has also been suggested that the Casimir effect in higher dimensions may be the underlying phenomenon that is responsible for the dark energy which is currently driving the accelerated expansion of the universe. In this paper we suggest that, in principle, it may be possible to directly manipulate the size of an extra dimension locally using Standard Model fields in the next ge...
Higher-dimensional bosonization and its application to Fermi liquids
Energy Technology Data Exchange (ETDEWEB)
Meier, Hendrik
2012-06-28
The bosonization scheme presented in this thesis allows to map models of interacting fermions onto equivalent models describing collective bosonic excitations. For simple systems that do not require plenty computational power and optimized algorithms, the positivity of the weight function in the bosonic frame has been confirmed - in particular also for those configurations in which the fermionic representation shows the minus-sign problem. The numerical tests are absolutely elementary and based on the simplest possible regularization scheme. The second part of this thesis presented an analytical study about the non-analytic corrections to thermodynamic quantities in a two-dimensional Fermi liquid. The perturbation theory developed for the exact formulation is by no means more convenient than the well-established fermionic diagram technique. The effective low-energy theory for studying the anomalous contributions to the Fermi liquid was derived focussing on the relevant soft modes of the interaction only. The final effective model took the form of a field theory for a bosonic superfield Ψ interacting in quadratic, cubic, and quartic terms in the action. This field theory turned out nontrivial and was shown to lead to logarithmic divergencies in both spin and charge channels. By means of a combined scheme of ladder diagram summations and renormalization group equations, the logarithmic terms were summed up in the first-loop order, thus yielding the renormalized effective coupling constants of the theory at low temperatures. The fully renormalized action then allowed to conveniently compute the low-temperature limit behavior of the non-analytic corrections to the Fermi-liquid thermodynamic response functions such as the low temperature non-analytic correction δc to the specific heat. The explicit formula for δc is the sum of two contributions - one due to the spin singlet and one due to the spin triplet superconducting excitations. Depending on the values of the
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
On the dimensional reduction of a gravitational theory containing higher-derivative terms
International Nuclear Information System (INIS)
Pollock, M.D.
1990-02-01
From the higher-dimensional gravitational theory L-circumflex=R-circumflex-2Λ-circumflex-α-circumflex 1 R-circumflex 2 =α-circumflex 2 R-circumflex AB R-circumflex AB -α-circumflex 3 R-circumflex ABCD R-circumflex ABCD , we derive the effective four-dimensional Lagrangian L. (author). 12 refs
A higher dimensional explanation of the excess of Higgs-like events at CERN LEP
Van der Bij, J J
2006-01-01
Searches for the SM Higgs boson by the four LEP experiments have found a 2.3 sigma excess at 98 GeV and a smaller 1.7 sigma at around 115 GeV. We interpret these excesses as evidence for a Higgs boson coupled to a higher dimensional singlet scalar. The fit implies a relatively low dimensional mixing scale mu_{lhd} 100 GeV. The data show a slight preference for a five-dimensional over a six-dimensional field. This Higgs boson cannot be seen at the LHC, but can be studied at the ILC.
CSIR Research Space (South Africa)
Mafu, M
2013-09-01
Full Text Available We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d + 1) mutually unbiased measurements in a...
The causal structure of spacetime is a parameterized Randers geometry
Energy Technology Data Exchange (ETDEWEB)
Skakala, Jozef; Visser, Matt, E-mail: jozef.skakala@msor.vuw.ac.nz, E-mail: matt.visser@msor.vuw.ac.nz [School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington (New Zealand)
2011-03-21
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
The causal structure of spacetime is a parameterized Randers geometry
International Nuclear Information System (INIS)
Skakala, Jozef; Visser, Matt
2011-01-01
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
Higher Dimensional Charged Black Hole Solutions in f(R Gravitational Theories
Directory of Open Access Journals (Sweden)
G. G. L. Nashed
2018-01-01
Full Text Available We present, without any assumption, a class of electric and magnetic flat horizon D-dimension solutions for a specific class of f(R=R+αR2, all of which behave asymptotically as Anti-de-Sitter spacetime. The most interesting property of these solutions is that the higher dimensions black holes, D>4, always have constant electric and magnetic charges in contrast to what is known in the literature. For D=4, we show that the magnetic field participates in the metric on equal foot as the electric field participates. Another interesting result is the fact that the Cauchy horizon is not identical with the event horizon. We use Komar formula to calculate the conserved quantities. We study the singularities and calculate the Hawking temperature and entropy and show that the first law of thermodynamics is always satisfied.
Minkowski Spacetime A Hundred Years Later
Petkov, Vesselin
2009-01-01
This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Space and Time" in 1909. His work on the spacetime representation of special relativity had a huge impact on the twentieth century physics to the extent that modern physics would be impossible without the notion of spacetime. While there is consensus on the mathematical significance of spacetime in theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. We owe Minkowski a clear answer to the question of the nature of spacetime -- whether it is only a mathematical space or represents a real four-dimensional world. A century after its publication the original Minkowski paper still represents an enrichment to the physicists, especially the relativists, who read it with the intent to fully investigate the depth of Minkowski's ideas on space and time and the physical meaning of special relativity. The volume begins with an excellent retranslation of Minkowski's ...
Exact geodesic distances in FLRW spacetimes
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.
The Historical Origins of Spacetime
Walter, Scott
The idea of spacetime investigated in this chapter, with a view toward understanding its immediate sources and development, is the one formulated and proposed by Hermann Minkowski in 1908. Until recently, the principle source used to form historical narratives of Minkowski's discovery of spacetime has been Minkowski's own discovery account, outlined in the lecture he delivered in Cologne, entitled Space and time [1]. Minkowski's lecture is usually considered as a bona fide first-person narrative of lived events. According to this received view, spacetime was a natural outgrowth of Felix Klein's successful project to promote the study of geometries via their characteristic groups of transformations. Or as Minkowski expressed the same basic thought himself, the theory of relativity discovered by physicists in 1905 could just as well have been proposed by some late-nineteenth-century mathematician, by simply reflecting upon the groups of transformations that left invariant the form of the equation of a propagating light wave. Minkowski's publications and research notes provide a contrasting picture of the discovery of spacetime, in which group theory plays no direct part. In order to relate the steps of Minkowski's discovery, we begin with an account of Poincaré's theory of gravitation, where Minkowski found some of the germs of spacetime. Poincaré's geometric interpretation of the Lorentz transformation is examined, along with his reasons for not pursuing a four-dimensional vector calculus. In the second section, Minkowski's discovery and presentation of the notion of a world line in spacetime is presented. In the third and final section, Poincaré's and Minkowski's diagrammatic interpretations of the Lorentz transformation are compared.
The applications of a higher-dimensional Lie algebra and its decomposed subalgebras
Yu, Zhang; Zhang, Yufeng
2009-01-01
With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra sμ(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras sμ(6) and E is used to directly construct integrable couplings. PMID:20084092
The applications of a higher-dimensional Lie algebra and its decomposed subalgebras
International Nuclear Information System (INIS)
Yu Zhang; Zhang Yufeng
2009-01-01
With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra sμ(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra sμ(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras sμ(6) and E is used to directly construct integrable couplings
The applications of a higher-dimensional Lie algebra and its decomposed subalgebras.
Yu, Zhang; Zhang, Yufeng
2009-01-15
With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra smu(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra smu(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras smu(6) and E is used to directly construct integrable couplings.
Hyperbolic statics in space-time
Pavlov, Dmitry; Kokarev, Sergey
2014-01-01
Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on...
Cosgrove, Joseph K
2018-01-01
In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in th...
Quasinormal modes in pure de Sitter spacetimes
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Du Daping; Wang Bin; Su Ruheng
2004-01-01
We have studied scalar perturbations as well as fermion perturbations in pure de Sitter spacetimes. For scalar perturbations we have shown that well-defined quasinormal modes in d-dimensions can exist provided that the mass of scalar field m>(d-1/2l). The quasinormal modes of fermion perturbations in three and four dimensional cases have also been investigated. We found that different from other dimensional cases, in the three dimensional pure de Sitter spacetime there is no quasinormal mode for the s-wave. This interesting difference caused by the spacial dimensions is true for both scalar and fermion perturbations
Axiomatics of uniform space-time models
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Levichev, A.V.
1983-01-01
The mathematical statement of space-time axiomatics of the special theory of relativity is given; it postulates that the space-time M is the binding single boundary Hausedorf local-compact four-dimensional topological space with the given order. The theorem is proved: if the invariant order in the four-dimensional group M is given by the semi-group P, which contingency K contains inner points , then M is commutative. The analogous theorem is correct for the group of two and three dimensionalities
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Pollock, M.D.
1988-01-01
We consider super-exponential inflation in the early universe, for which H 2 /H = q >> 1, with particular reference to the higher-dimensional theory of Shafi and Wetterich, which is discussed in further detail. The Hubble parameter H is given by H 2 ≅ (8π/3m P 2 )V(Φ), where the ''inflation'' field Φ is related to the radius of the internal space, and obeys the equation of motion 3HΦ ≅ -dW/dΦ. The spectrum of density perturbations is given by δρ/ρ = (M/M 0 ) -s , where s -1 ≅ 3(q + 1); and X = (-dV/dΦ)/(dW/dΦ). The parameters q and X are both positive constants, hence the need for two distinct potentials, which can be met in a higher-dimensional theory with higher-derivative terms R 2 = α 1 R 2 + α 2 R AB R AB + α 3 R ABCD R ABCD . Some fine-tuning of the parameters α i and/or of the cosmological constant Λ is always necessary in order to have super-exponential inflation. It is possible to obtain a spectrum of density perturbations with s > or approx. 1/20, which helps to give agreement with observations of the cosmic microwave background radiation at very large scales ∝ 1000 Mpc. When R 2 is proportional to the Euler number density, making the four-dimensional theory free of ghosts, then super-exponential inflation is impossible, but a phase of inflation with H < 0 can still occur. (orig.)
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Chu, Yi-Zen
2014-01-01
Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes – particularly around black holes – we show how, for certain classes of geometries, one might obtain its retarded or advanced minimally coupled massless scalar Green's function by using the corresponding Green's functions in the higher dimensional Minkowski spacetime where it is embedded. Analogous statements hold for certain classes of curved Riemannian spaces, with positive definite metrics, which may be embedded in higher dimensional Euclidean spaces. The general formula is applied to (d ≥ 2)-dimensional de Sitter spacetime, and the scalar Green's function is demonstrated to be sourced by a line emanating infinitesimally close to the origin of the ambient (d + 1)-dimensional Minkowski spacetime and piercing orthogonally through the de Sitter hyperboloids of all finite sizes. This method does not require solving the de Sitter wave equation directly. Only the zero mode solution to an ordinary differential equation, the “wave equation” perpendicular to the hyperboloid – followed by a one-dimensional integral – needs to be evaluated. A topological obstruction to the general construction is also discussed by utilizing it to derive a generalized Green's function of the Laplacian on the (d ≥ 2)-dimensional sphere
Energy Technology Data Exchange (ETDEWEB)
Nomura, Yasunori [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, Kashiwa 277-8583 (Japan); Salzetta, Nico, E-mail: nsalzetta@berkeley.edu [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sanches, Fabio; Weinberg, Sean J. [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2016-12-10
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.
Schure, Mark R; Davis, Joe M
2017-11-10
Orthogonality metrics (OMs) for three and higher dimensional separations are proposed as extensions of previously developed OMs, which were used to evaluate the zone utilization of two-dimensional (2D) separations. These OMs include correlation coefficients, dimensionality, information theory metrics and convex-hull metrics. In a number of these cases, lower dimensional subspace metrics exist and can be readily calculated. The metrics are used to interpret previously generated experimental data. The experimental datasets are derived from Gilar's peptide data, now modified to be three dimensional (3D), and a comprehensive 3D chromatogram from Moore and Jorgenson. The Moore and Jorgenson chromatogram, which has 25 identifiable 3D volume elements or peaks, displayed good orthogonality values over all dimensions. However, OMs based on discretization of the 3D space changed substantially with changes in binning parameters. This example highlights the importance in higher dimensions of having an abundant number of retention times as data points, especially for methods that use discretization. The Gilar data, which in a previous study produced 21 2D datasets by the pairing of 7 one-dimensional separations, was reinterpreted to produce 35 3D datasets. These datasets show a number of interesting properties, one of which is that geometric and harmonic means of lower dimensional subspace (i.e., 2D) OMs correlate well with the higher dimensional (i.e., 3D) OMs. The space utilization of the Gilar 3D datasets was ranked using OMs, with the retention times of the datasets having the largest and smallest OMs presented as graphs. A discussion concerning the orthogonality of higher dimensional techniques is given with emphasis on molecular diversity in chromatographic separations. In the information theory work, an inconsistency is found in previous studies of orthogonality using the 2D metric often identified as %O. A new choice of metric is proposed, extended to higher dimensions
Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds
International Nuclear Information System (INIS)
Saharian, Aram A.
2006-01-01
We investigate the vacuum expectation value of the surface energy-momentum tensor for a massive scalar field with general curvature coupling parameter obeying the Robin boundary conditions on two codimension one parallel branes in a (D+1)-dimensional background spacetime AdS D 1 +1 xΣ with a warped internal space Σ. These vacuum densities correspond to a gravitational source of the cosmological constant type for both subspaces of the branes. Using the generalized zeta function technique in combination with contour integral representations, the surface energies on the branes are presented in the form of the sum of single-brane and second-brane-induced parts. For the geometry of a single brane both regions, on the left and on the right of the brane, are considered. At the physical point the corresponding zeta functions contain pole and finite contributions. For an infinitely thin brane taking these regions together, in odd spatial dimensions the pole parts cancel and the total zeta function is finite. The renormalization procedure for the surface energies and the structure of the corresponding counterterms are discussed. The parts in the surface densities generated by the presence of the second brane are finite for all nonzero values of the interbrane separation and are investigated in various asymptotic regions of the parameters. In particular, it is shown that for large distances between the branes the induced surface densities give rise to an exponentially suppressed cosmological constant on the brane. The total energy of the vacuum including the bulk and boundary contributions is evaluated by the zeta function technique and the energy balance between separate parts is discussed
International Nuclear Information System (INIS)
Larsen, A.L.; Sanchez, N.
1996-01-01
We find that the fundamental quadratic form of classical string propagation in (2+1)-dimensional constant curvature spacetimes solves the sinh-Gordon equation, the cosh-Gordon equation, or the Liouville equation. We show that in both de Sitter and anti endash de Sitter spacetimes (as well as in the 2+1 black hole anti endash de Sitter spacetime), all three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multistring solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti endash de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the sinh-Gordon equation, the cosh-Gordon equation, and the Liouville equation by their higher dimensional generalizations. copyright 1996 The American Physical Society
Macroscopic Spacetime Shortcuts in the Manyfold Universe
Loup, F
2004-01-01
Recently the idea of a Manyfold Universe was proposed by some authors to explain Dark Matter . In this study we assume that the Standard Model(SM) of particles and fields with gravity propagating in the Higher Dimensional Spacetime(Bulk) while other interactions are confined to 3+1 Einsteinian spacetime(Brane) is not due to open strings and closed loops but instead is due to the capability of gravity as the weakest and "smallest" interaction to penetrate these small Bulk size ($10^{-31}$m to $10^{-35}$m) while protons,neutrons and other interactions stronger and "larger" than gravity do not "fits" in the size of the Bulk and remains trapped on the Brane and we present a equation to justify this point of view. Our picture relies over the geometrical beauty of the Manyfold Universe proposal that Dark Matter is chemically identical to ordinary matter but lies on other Folds. Also the geometrical point of view for the small size of the Bulk eliminates the need of trapping mechanisms to confine matter in the Brane...
A short history of fractal-Cantorian space-time
International Nuclear Information System (INIS)
Marek-Crnjac, L.
2009-01-01
The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.
Thermal dimension of quantum spacetime
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Amelino-Camelia, Giovanni, E-mail: amelino@roma1.infn.it [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy); Brighenti, Francesco [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Dipartimento di Fisica e Astronomia dell' Università di Bologna and Sez. Bologna INFN, Via Irnerio 46, 40126 Bologna (Italy); Gubitosi, Giulia [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Santos, Grasiele [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)
2017-04-10
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of “dynamical dimensional reduction” which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the “spectral dimension”, which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the “thermal dimension” which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.
Rotating spacetimes with asymptotic nonflat structure and the gyromagnetic ratio
International Nuclear Information System (INIS)
Aliev, Alikram N.
2008-01-01
In general relativity, the gyromagnetic ratio for all stationary, axisymmetric, and asymptotically flat Einstein-Maxwell fields is known to be g=2. In this paper, we continue our previous works of examination of this result for rotating charged spacetimes with asymptotic nonflat structure. We first consider two instructive examples of these spacetimes: The spacetime of a Kerr-Newman black hole with a straight cosmic string on its axis of symmetry and the Kerr-Newman Taub-NUT (Newman-Unti-Tamburino) spacetime. We show that for both spacetimes the gyromagnetic ratio g=2 independent of their asymptotic structure. We also extend this result to a general class of metrics which admit separation of variables for the Hamilton-Jacobi and wave equations. We proceed with the study of the gyromagnetic ratio in higher dimensions by considering the general solution for rotating charged black holes in minimal five-dimensional gauged supergravity. We obtain the analytic expressions for two distinct gyromagnetic ratios of these black holes that are associated with their two independent rotation parameters. These expressions reveal the dependence of the gyromagnetic ratio on both the curvature radius of the AdS background and the parameters of the black holes: The mass, electric charge, and two rotation parameters. We explore some special cases of interest and show that when the two rotation parameters are equal to each other and the rotation occurs at the maximum angular velocity, the gyromagnetic ratio g=4 regardless of the value of the electric charge. This agrees precisely with our earlier result obtained for general Kerr-AdS black holes with a test electric charge. We also show that in the Bogomol'nyi-Prasad-Sommerfield (BPS) limit the gyromagnetic ratio for a supersymmetric black hole with equal rotation parameters ranges between 2 and 4
International Nuclear Information System (INIS)
Naumis, Gerardo G.; Bazan, A.; Torres, M.; Aragon, J.L.; Quintero-Torres, R.
2008-01-01
One of the few examples in which the physical properties of an incommensurable system reflect an underlying higher dimensionality is presented. Specifically, we show that the reflectivity distribution of an incommensurable one-dimensional cavity is given by the density of states of a tight-binding Hamiltonian in a two-dimensional triangular lattice. Such effect is due to an independent phase decoupling of the scattered waves, produced by the incommensurable nature of the system, which mimics a random noise generator. This principle can be applied to design a cavity that avoids resonant reflections for almost any incident wave. An optical analogy, by using three mirrors with incommensurable distances between them, is also presented. Such array produces a countable infinite fractal set of reflections, a phenomena which is opposite to the effect of optical invisibility
International Nuclear Information System (INIS)
Harada, Tomohiro; Nakao, Ken-ichi
2004-01-01
It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its visibility. The visible border, corresponding to the naked singularity, is not only relevant to mathematical completeness of general relativity but also a window into new physics in strongly curved spacetimes, which is in principle observable
Classification of the Weyl tensor in higher dimensions and applications
International Nuclear Information System (INIS)
Coley, A
2008-01-01
We review the theory of alignment in Lorentzian geometry and apply it to the algebraic classification of the Weyl tensor in higher dimensions. This classification reduces to the well-known Petrov classification of the Weyl tensor in four dimensions. We discuss the algebraic classification of a number of known higher dimensional spacetimes. There are many applications of the Weyl classification scheme, especially when used in conjunction with the higher dimensional frame formalism that has been developed in order to generalize the four-dimensional Newman-Penrose formalism. For example, we discuss higher dimensional generalizations of the Goldberg-Sachs theorem and the peeling theorem. We also discuss the higher dimensional Lorentzian spacetimes with vanishing scalar curvature invariants and constant scalar curvature invariants, which are of interest since they are solutions of supergravity theory. (topical review)
Feynman propagator and space-time transformation technique
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Nassar, A.B.
1987-01-01
We evaluate the exact propagator for the time-dependent two-dimensional charged harmonic oscillator in a time-varying magnetic field, by taking direct recourse to the corresponding Schroedinger equation. Through the usage of an appropriate space-time transformation, we show that such a propagator can be obtained from the free propagator in the new space-time coordinate system. (orig.)
Fu, Yuchen; Shelley-Abrahamson, Seth
2016-06-01
We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for U_q(sl_N). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov.
Using Harry Potter to Bridge Higher Dimensionality in Mathematics and High-interest Literature
Boerman-Cornell, William; Klanderman, David; Schut, Alexa
2017-01-01
The Harry Potter series is a favorite for out-of-school reading and has been used in school, largely as an object of study in language arts. Using a content analysis to highlight the ways in which J.K. Rowling's work could be used to teach higher dimensionality in math, the authors argues that the content is sufficient in such books to engage the…
Higher dimensional quantum Hall effect as A-class topological insulator
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Hasebe, Kazuki, E-mail: khasebe@stanford.edu
2014-09-15
We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry. There are two different formulations of non-commutative geometry for higher dimensional fuzzy spheres: the ordinary commutator formulation and quantum Nambu bracket formulation. Corresponding to these formulations, we introduce two kinds of monopole gauge fields: non-abelian gauge field and antisymmetric tensor gauge field, which respectively realize the non-commutative geometry of fuzzy sphere in the lowest Landau level. We establish connection between the two types of monopole gauge fields through Chern–Simons term, and derive explicit form of tensor monopole gauge fields with higher string-like singularity. The connection between two types of monopole is applied to generalize the concept of flux attachment in quantum Hall effect to A-class topological insulator. We propose tensor type Chern–Simons theory as the effective field theory for membranes in A-class topological insulators. Membranes turn out to be fractionally charged objects and the phase entanglement mediated by tensor gauge field transforms the membrane statistics to be anyonic. The index theorem supports the dimensional hierarchy of A-class topological insulator. Analogies to D-brane physics of string theory are discussed too.
Antigravity from a spacetime defect
Klinkhamer, F. R.; Queiruga, J. M.
2018-01-01
We argue that there may exist spacetime defects embedded in Minkowski spacetime, which have negative active gravitational mass. One such spacetime defect then repels a test particle, corresponding to what may be called "antigravity."
Higher dimensional operator corrections to the goldstino Goldberger-Treiman vertices
International Nuclear Information System (INIS)
Lee, T.
2000-01-01
The goldstino-matter interactions given by the Goldberger-Treiman relations can receive higher dimensional operator corrections of O(q 2 /M 2 ), where M denotes the mass of the mediators through which SUSY breaking is transmitted. These corrections in the gauge mediated SUSY breaking models arise from loop diagrams, and an explicit calculation of such corrections is presented. It is emphasized that the Goldberger-Treiman vertices are valid only below the mediator scale, and at higher energies goldstinos decouple from the MSSM fields. The implication of this fact for gravitino cosmology in GMSB models is mentioned. (orig.)
Higher order BLG supersymmetry transformations from 10-dimensional super Yang Mills
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Hall, John [Alumnus of Physics Department, Imperial College,South Kensington, London, SW7 2AZ (United Kingdom); Low, Andrew [Physics Department, Wimbledon High School,Mansel Road, London, SW19 4AB (United Kingdom)
2014-06-26
We study a Simple Route for constructing the higher order Bagger-Lambert-Gustavsson theory - both supersymmetry transformations and Lagrangian - starting from knowledge of only the 10-dimensional Super Yang Mills Fermion Supersymmetry transformation. We are able to uniquely determine the four-derivative order corrected supersymmetry transformations, to lowest non-trivial order in Fermions, for the most general three-algebra theory. For the special case of Euclidean three-algbera, we reproduce the result presented in arXiv:1207.1208, with significantly less labour. In addition, we apply our method to calculate the quadratic fermion terms in the higher order BLG fermion supersymmetry transformation.
Singularities in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept
Czech Academy of Sciences Publication Activity Database
Hervik, S.; Málek, Tomáš; Pravda, Vojtěch; Pravdová, Alena
2015-01-01
Roč. 32, č. 24 (2015), s. 245012 ISSN 0264-9381 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : einstein spacetimes * generalized gravities * universal spacetimes Subject RIV: BA - General Mathematics Impact factor: 2.837, year: 2015 http://iopscience.iop.org/article/10.1088/0264-9381/32/24/245012
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.
Extra-Dimensional “Metamaterials”: A Model of Inflation Due to a Metric Signature Transition
Directory of Open Access Journals (Sweden)
Igor I. Smolyaninov
2017-09-01
Full Text Available Lattices of topological defects, such as Abrikosov lattices and domain wall lattices, often arise as metastable ground states in higher-dimensional field theoretical models. We demonstrate that such lattice states may be described as extra-dimensional “metamaterials” via higher-dimensional effective medium theory. A 4 + 1 dimensional extension of Maxwell electrodynamics with a compactified time-like dimension is considered as an example. It is demonstrated that from the point of view of macroscopic electrodynamics an Abrikosov lattice state in such a 4 + 1 dimensional spacetime may be described as a uniaxial hyperbolic medium. Extraordinary photons perceive this medium as a 3 + 1 dimensional Minkowski spacetime in which one of the original spatial dimensions plays the role of a new time-like coordinate. Since the metric signature of this effective spacetime depends on the Abrikosov lattice periodicity, the described model may be useful in studying metric signature transitions.
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)
Nomura, Yasunori; Rath, Pratik; Salzetta, Nico
2018-05-01
The past decade has seen a tremendous effort toward unraveling the relationship between entanglement and emergent spacetime. These investigations have revealed that entanglement between holographic degrees of freedom is crucial for the existence of bulk spacetime. We examine this connection from the other end of the entanglement spectrum and clarify the assertion that maximally entangled states have no reconstructable spacetime. To do so, we first define the conditions for bulk reconstructability. Under these terms, we scrutinize two cases of maximally entangled holographic states. One is the familiar example of AdS black holes; these are dual to thermal states of the boundary conformal field theory. Sending the temperature to the cutoff scale makes the state maximally entangled and the respective black hole consumes the spacetime. We then examine the de Sitter limit of Friedmann-Robertson-Walker (FRW) spacetimes. This limit is maximally entangled if one formulates the boundary theory on the holographic screen. Paralleling the anti-de Sitter (AdS) black hole, we find the resulting reconstructable region of spacetime vanishes. Motivated by these results, we prove a theorem showing that maximally entangled states have no reconstructable spacetime. Evidently, the emergence of spacetime is endemic to intermediate entanglement. By studying the manner in which intermediate entanglement is achieved, we uncover important properties about the boundary theory of FRW spacetimes. With this clarified understanding, our final discussion elucidates the natural way in which holographic Hilbert spaces may house states dual to different geometries. This paper provides a coherent picture clarifying the link between spacetime and entanglement and develops many promising avenues of further work.
Bulk emission by higher-dimensional black holes: almost perfect blackbody radiation
International Nuclear Information System (INIS)
Hod, Shahar
2011-01-01
We study the Hawking radiation emitted into the bulk by (D + 1)-dimensional Schwarzschild black holes. It is well known that the black-hole spectrum departs from exact blackbody form due to the frequency dependence of the 'greybody' factors. For intermediate values of D (3 ≤ D ∼ > 1, the typical wavelengths in the black-hole spectrum are much shorter than the size of the black hole. In this regime, the greybody factors are well described by the geometric-optics approximation according to which they are almost frequency independent. Following this observation, we argue that for higher-dimensional black holes with D >> 1, the total power emitted into the bulk should be well approximated by the analytical formula for perfect blackbody radiation. We test the validity of this analytical prediction with numerical computations.
Twistor Cosmology and Quantum Space-Time
International Nuclear Information System (INIS)
Brody, D.C.; Hughston, L.P.
2005-01-01
The purpose of this paper is to present a model of a 'quantum space-time' in which the global symmetries of space-time are unified in a coherent manner with the internal symmetries associated with the state space of quantum-mechanics. If we take into account the fact that these distinct families of symmetries should in some sense merge and become essentially indistinguishable in the unified regime, our framework may provide an approximate description of or elementary model for the structure of the universe at early times. The quantum elements employed in our characterisation of the geometry of space-time imply that the pseudo-Riemannian structure commonly regarded as an essential feature in relativistic theories must be dispensed with. Nevertheless, the causal structure and the physical kinematics of quantum space-time are shown to persist in a manner that remains highly analogous to the corresponding features of the classical theory. In the case of the simplest conformally flat cosmological models arising in this framework, the twistorial description of quantum space-time is shown to be effective in characterising the various physical and geometrical properties of the theory. As an example, a sixteen-dimensional analogue of the Friedmann-Robertson-Walker cosmologies is constructed, and its chronological development is analysed in some detail. More generally, whenever the dimension of a quantum space-time is an even perfect square, there exists a canonical way of breaking the global quantum space-time symmetry so that a generic point of quantum space-time can be consistently interpreted as a quantum operator taking values in Minkowski space. In this scenario, the breakdown of the fundamental symmetry of the theory is due to a loss of quantum entanglement between space-time and internal quantum degrees of freedom. It is thus possible to show in a certain specific sense that the classical space-time description is an emergent feature arising as a consequence of a
Cosmic censorship in higher dimensions
International Nuclear Information System (INIS)
Goswami, Rituparno; Joshi, Pankaj S.
2004-01-01
We show that the naked singularities arising in dust collapse from smooth initial data (which include those discovered by Eardley and Smarr, Christodoulou, and Newman) are removed when we make a transition to higher dimensional spacetimes. Cosmic censorship is then restored for dust collapse, which will always produce a black hole as the collapse end state for dimensions D≥6, under conditions to be motivated physically such as the smoothness of initial data from which the collapse develops
Energy Technology Data Exchange (ETDEWEB)
Li, Hui-Ling [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China); Feng, Zhong-Wen [China West Normal University, College of Physics and Space Science, Nanchong (China); Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China)
2018-01-15
With motivation by holography, employing black hole entropy, two-point connection function and entanglement entropy, we show that, for the higher-dimensional Anti-de Sitter charged hairy black hole in the fixed charged ensemble, a Van der Waals-like phase transition can be observed. Furthermore, based on the Maxwell equal-area construction, we check numerically the equal-area law for a first order phase transition in order to further characterize the Van der Waals-like phase transition. (orig.)
Directory of Open Access Journals (Sweden)
Muhammad Aslam Noor
2008-01-01
Full Text Available We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM. We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.
A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
International Nuclear Information System (INIS)
Davis, Paul
2006-01-01
In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable
International Nuclear Information System (INIS)
Li, Hui-Ling; Feng, Zhong-Wen; Zu, Xiao-Tao
2018-01-01
With motivation by holography, employing black hole entropy, two-point connection function and entanglement entropy, we show that, for the higher-dimensional Anti-de Sitter charged hairy black hole in the fixed charged ensemble, a Van der Waals-like phase transition can be observed. Furthermore, based on the Maxwell equal-area construction, we check numerically the equal-area law for a first order phase transition in order to further characterize the Van der Waals-like phase transition. (orig.)
Grand unified theory precursors and nontrivial fixed points in higher-dimensional gauge theories
International Nuclear Information System (INIS)
Dienes, Keith R.; Dudas, Emilian; Gherghetta, Tony
2003-01-01
Within the context of traditional logarithmic grand unification at M GUT ≅10 16 GeV, we show that it is nevertheless possible to observe certain GUT states such as X and Y gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as 'GUT precursors'. These states offer an interesting alternative possibility for new physics at the TeV scale, and could be used to directly probe GUT physics even though the scale of gauge coupling unification remains high. Our results also give rise to a Kaluza-Klein realization of nontrivial fixed points in higher-dimensional gauge theories
Spontaneous symmetry breaking and fermion chirality in higher-dimensional gauge theory
International Nuclear Information System (INIS)
Wetterich, C.
1985-01-01
The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to H=SU(3)sub(C)xSU(2)sub(L)xU(1)sub(R)xU(1)sub(B-L). For all solutions, the fermions which are chiral with respect to H form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)sub(G)xU(1)sub(G). For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)sub(G)xU(1)sub(G). Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories. (orig.)
An, Xinliang; Wong, Willie Wai Yeung
2018-01-01
Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first give a systematic presentation of the main geometric constructions, with emphasis on the Kodama vector field and the Hawking energy; the construction is signature independent. This leads to proofs of general Birkhoff-type theorems for warped product manifolds; our theorems in particular apply to situations where the warped product manifold is not necessarily Einstein, and thus can be applied to solutions with matter content in general relativity. Next we specialize to the Lorentzian case and study the propagation of null expansions under the assumption of the dominant energy condition. We prove several non-existence results relating to the Yamabe class of the fibers, in the spirit of the black-hole topology theorem of Hawking–Galloway–Schoen. Finally we discuss the effect of the warped product ansatz on matter models. In particular we construct several cosmological solutions to the Einstein–Euler equations whose spatial geometry is generally not isotropic.
Spacetime representation of topological phononics
Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.
2018-05-01
Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.
Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Podolský, J.; Žofka, M.
2015-01-01
Roč. 2015, č. 2 (2015), 045 ISSN 1029-8479 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : Einstein-Maxwell spacetimes * classical theories of gravity * black holes Subject RIV: BA - General Mathematics Impact factor: 6.023, year: 2015 http://link.springer.com/article/10.1007/JHEP02%282015%29045
Upper Estimates on the Higher-dimensional Multifractal Spectrum of Local Entropy%局部熵高维重分形谱的上界估计
Institute of Scientific and Technical Information of China (English)
严珍珍; 陈二才
2008-01-01
We discuss the problem of higher-dimensional multifractal spectrum of lo-cal entropy for arbitrary invariant measures. By utilizing characteristics of a dynam-ical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the higher-dimensional mul-tifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractal spetrum of entropies.
Identifying Talent in Youth Sport: A Novel Methodology Using Higher-Dimensional Analysis
Till, Kevin; Jones, Ben L.; Cobley, Stephen; Morley, David; O'Hara, John; Chapman, Chris; Cooke, Carlton; Beggs, Clive B.
2016-01-01
Prediction of adult performance from early age talent identification in sport remains difficult. Talent identification research has generally been performed using univariate analysis, which ignores multivariate relationships. To address this issue, this study used a novel higher-dimensional model to orthogonalize multivariate anthropometric and fitness data from junior rugby league players, with the aim of differentiating future career attainment. Anthropometric and fitness data from 257 Under-15 rugby league players was collected. Players were grouped retrospectively according to their future career attainment (i.e., amateur, academy, professional). Players were blindly and randomly divided into an exploratory (n = 165) and validation dataset (n = 92). The exploratory dataset was used to develop and optimize a novel higher-dimensional model, which combined singular value decomposition (SVD) with receiver operating characteristic analysis. Once optimized, the model was tested using the validation dataset. SVD analysis revealed 60 m sprint and agility 505 performance were the most influential characteristics in distinguishing future professional players from amateur and academy players. The exploratory dataset model was able to distinguish between future amateur and professional players with a high degree of accuracy (sensitivity = 85.7%, specificity = 71.1%; ptalent identification. PMID:27224653
Identifying Talent in Youth Sport: A Novel Methodology Using Higher-Dimensional Analysis.
Till, Kevin; Jones, Ben L; Cobley, Stephen; Morley, David; O'Hara, John; Chapman, Chris; Cooke, Carlton; Beggs, Clive B
2016-01-01
Prediction of adult performance from early age talent identification in sport remains difficult. Talent identification research has generally been performed using univariate analysis, which ignores multivariate relationships. To address this issue, this study used a novel higher-dimensional model to orthogonalize multivariate anthropometric and fitness data from junior rugby league players, with the aim of differentiating future career attainment. Anthropometric and fitness data from 257 Under-15 rugby league players was collected. Players were grouped retrospectively according to their future career attainment (i.e., amateur, academy, professional). Players were blindly and randomly divided into an exploratory (n = 165) and validation dataset (n = 92). The exploratory dataset was used to develop and optimize a novel higher-dimensional model, which combined singular value decomposition (SVD) with receiver operating characteristic analysis. Once optimized, the model was tested using the validation dataset. SVD analysis revealed 60 m sprint and agility 505 performance were the most influential characteristics in distinguishing future professional players from amateur and academy players. The exploratory dataset model was able to distinguish between future amateur and professional players with a high degree of accuracy (sensitivity = 85.7%, specificity = 71.1%; ptalent identification.
Generating asymptotically plane wave spacetimes
International Nuclear Information System (INIS)
Hubeny, Veronika E.; Rangamani, Mukund
2003-01-01
In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line. (author)
International Nuclear Information System (INIS)
Dodson, C.T.J.
1977-02-01
This is the second part of a monograph intended to be a mathematically rigorous account of the current position of the bundle-completion of spacetime in general relativity; some new material is included
International Nuclear Information System (INIS)
Racz, I.
1991-09-01
The problem of the existence of local extensions of spacetime is considered. It is shown that for a spacetime including an incomplete inextendible non-coiling causal geodesic curve there exists a particular C k (resp. C k- ) local extension provided that the curvature and its covariant derivatives are well behaved up to order k + 1 (resp. k) along a family of causal geodetics (around the chosen one). (R.P.) 15 refs
On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations
International Nuclear Information System (INIS)
Westerberg, A.
1997-01-01
We discuss a previously discovered extension of the infinite-dimensional Lie algebra map(M,g) which generalizes the Kac-Moody algebras in 1+1 dimensions and the Mickelsson-Faddeev algebras in 3+1 dimensions to manifolds M of general dimensions. Furthermore, we review the method of regularizing current algebras in higher dimensions using pseudodifferential operator (PSDO) symbol calculus. In particular, we discuss the issue of Lie algebra cohomology of PSDOs and its relation to the Schwinger terms arising in the quantization process. Finally, we apply this regularization method to the algebra with partial success, and discuss the remaining obstacles to the construction of a Fock space representation. (orig.)
The effective action for edge states in higher-dimensional quantum Hall systems
International Nuclear Information System (INIS)
Karabali, Dimitra; Nair, V.P.
2004-01-01
We show that the effective action for the edge excitations of a quantum Hall droplet of fermions in higher dimensions is generically given by a chiral bosonic action. We explicitly analyze the quantum Hall effect on complex projective spaces CP k , with a U(1) background magnetic field. The edge excitations are described by Abelian bosonic fields on S 2k-1 with only one spatial direction along the boundary of the droplet relevant for the dynamics. Our analysis also leads to an action for edge excitations for the case of the Zhang-Hu four-dimensional quantum Hall effect defined on S 4 with an SU(2) background magnetic field, using the fact that CP 3 is an S 2 -bundle over S 4
Thick domain wall spacetimes with and without reflection symmetry
International Nuclear Information System (INIS)
Melfo, Alejandra; Pantoja, Nelson; Skirzewski, Aureliano
2003-01-01
We show that different thick domain wall spacetimes, for which the scalar field configuration and the potential are the same, can be found as solutions to the coupled Einstein-scalar field equations, depending on whether or not reflection symmetry on the wall is imposed. Spacetimes with reflection symmetry may be dynamic or static, while the asymmetric ones are static. Asymmetric walls are asymptotically flat on one side and reduce to the Taub spacetime on the other. Examples of asymmetric thick walls in D-dimensional spacetimes are given, and previous analysis on the distributional thin-wall limit of the dynamic symmetric thick walls are extended to the asymmetric case. A new family of reflection symmetric, static thick domain wall spacetimes, including previously known Bogomol'nyi-Prasad-Sommerfield walls, is presented
Identifying Talent in Youth Sport: A Novel Methodology Using Higher-Dimensional Analysis.
Directory of Open Access Journals (Sweden)
Kevin Till
Full Text Available Prediction of adult performance from early age talent identification in sport remains difficult. Talent identification research has generally been performed using univariate analysis, which ignores multivariate relationships. To address this issue, this study used a novel higher-dimensional model to orthogonalize multivariate anthropometric and fitness data from junior rugby league players, with the aim of differentiating future career attainment. Anthropometric and fitness data from 257 Under-15 rugby league players was collected. Players were grouped retrospectively according to their future career attainment (i.e., amateur, academy, professional. Players were blindly and randomly divided into an exploratory (n = 165 and validation dataset (n = 92. The exploratory dataset was used to develop and optimize a novel higher-dimensional model, which combined singular value decomposition (SVD with receiver operating characteristic analysis. Once optimized, the model was tested using the validation dataset. SVD analysis revealed 60 m sprint and agility 505 performance were the most influential characteristics in distinguishing future professional players from amateur and academy players. The exploratory dataset model was able to distinguish between future amateur and professional players with a high degree of accuracy (sensitivity = 85.7%, specificity = 71.1%; p<0.001, although it could not distinguish between future professional and academy players. The validation dataset model was able to distinguish future professionals from the rest with reasonable accuracy (sensitivity = 83.3%, specificity = 63.8%; p = 0.003. Through the use of SVD analysis it was possible to objectively identify criteria to distinguish future career attainment with a sensitivity over 80% using anthropometric and fitness data alone. As such, this suggests that SVD analysis may be a useful analysis tool for research and practice within talent identification.
Infinite-parametric extension of the conformal algebra in D>2 space-time dimension
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-09-01
On the basis of the analytic continuations of semisimple Lie algebras discovered recently by us we construct manifestly quasiconformal infinite-dimensional algebras AC(so(4,1)) and PAC(so(3,2)) extending the conformal algebras in three-dimensional Euclidean and Minkowski space-time like the Virasoro algebra extends so(2,1). Their higher spin generalizations are also constructed. A counterpart of the central extension for D>2 and possible applications in exactly solvable conformal quantum field models in D>2 are discussed. (author). 31 refs, 2 figs
Energy Technology Data Exchange (ETDEWEB)
Lippoldt, Stefan
2016-01-21
In this thesis we study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin base transformations. We emphasize the advantages of the spin base invariant formalism both from a conceptual as well as from a practical viewpoint. This suggests that local spin base invariance should be added to the list of (effective) properties of (quantum) gravity theories. We find support for this viewpoint by the explicit construction of a global realization of the Clifford algebra on a 2-sphere which is impossible in the spin-base non-invariant vielbein formalism. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vielbein field is not required. We disclose the hidden spin base invariance of the vielbein formalism. Explicit formulas for the spin connection as a function of the Dirac matrices are found. This connection consists of a canonical part that is completely fixed in terms of the Dirac matrices and a free part that can be interpreted as spin torsion. The common Lorentz symmetric gauge for the vielbein is constructed for the Dirac matrices, even for metrics which are not linearly connected. Under certain criteria, it constitutes the simplest possible gauge, demonstrating why this gauge is so useful. Using the spin base formulation for building a field theory of quantized gravity and matter fields, we show that it suffices to quantize the metric and the matter fields. This observation is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions. Hence, in the second part of this thesis we critically examine the gauge, and the field-parametrization dependence of renormalization group flows in the vicinity of non-Gaussian fixed points in quantum gravity. While physical
Singularities in FLRW spacetimes
het Lam, Huibert; Prokopec, Tomislav
2017-12-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.
Symmetry, structure, and spacetime
Rickles, Dean
2007-01-01
In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational
Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul
2016-08-01
Numerical solutions of the hydrodynamical model of semiconductor devices are presented in one and two-space dimension. The model describes the charge transport in semiconductor devices. Mathematically, the models can be written as a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the conservation element and solution element (CE/SE) method for hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results of the suggested scheme are compared with the splitting scheme based on Nessyahu-Tadmor (NT) central scheme for convection step and the same semi-implicit scheme for the relaxation step. The effects of various parameters such as low field mobility, device length, lattice temperature and voltages for one-space dimensional hydrodynamic model are explored to further validate the generic applicability of the CE/SE method for the current model equations. A two dimensional simulation is also performed by CE/SE method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.
Three-dimensional freak waves and higher-order wave-wave resonances
Badulin, S. I.; Ivonin, D. V.; Dulov, V. A.
2012-04-01
Quite often the freak wave phenomenon is associated with the mechanism of modulational (Benjamin-Feir) instability resulted from resonances of four waves with close directions and scales. This weakly nonlinear model reflects some important features of the phenomenon and is discussing in a great number of studies as initial stage of evolution of essentially nonlinear water waves. Higher-order wave-wave resonances attract incomparably less attention. More complicated mathematics and physics explain this disregard partially only. The true reason is a lack of adequate experimental background for the study of essentially three-dimensional water wave dynamics. We start our study with the classic example of New Year Wave. Two extreme events: the famous wave 26.5 meters and one of smaller 18.5 meters height (formally, not freak) of the same record, are shown to have pronounced features of essentially three-dimensional five-wave resonant interactions. The quasi-spectra approach is used for the data analysis in order to resolve adequately frequencies near the spectral peak fp ≈ 0.057Hz and, thus, to analyze possible modulations of the dominant wave component. In terms of the quasi-spectra the above two anomalous waves show co-existence of the peak harmonic and one at frequency f5w = 3/2fp that corresponds to maximum of five-wave instability of weakly nonlinear waves. No pronounced marks of usually discussed Benjamin-Feir instability are found in the record that is easy to explain: the spectral peak frequency fp corresponds to the non-dimensional depth parameter kD ≈ 0.92 (k - wavenumber, D ≈ 70 meters - depth at the Statoil platform Draupner site) that is well below the shallow water limit of the instability kD = 1.36. A unique data collection of wave records of the Marine Hydrophysical Institute in the Katsiveli platform (Black Sea) has been analyzed in view of the above findings of possible impact of the five-wave instability on freak wave occurrence. The data cover
Cauchy horizons in Gowdy spacetimes
International Nuclear Information System (INIS)
Chrusciel, Piotr T; Lake, Kayll
2004-01-01
We analyse exhaustively the structure of non-degenerate Cauchy horizons in Gowdy spacetimes, and we establish existence of a large class of non-polarized Gowdy spacetimes with such horizons. Our results here, together with the deep new results of Ringstroem, establish strong cosmic censorship in (toroidal) Gowdy spacetimes
Towards realistic models from Higher-Dimensional theories with Fuzzy extra dimensions
Gavriil, D.; Zoupanos, G.
2014-01-01
We briefly review the Coset Space Dimensional Reduction (CSDR) programme and the best model constructed so far and then we present some details of the corresponding programme in the case that the extra dimensions are considered to be fuzzy. In particular, we present a four-dimensional $\\mathcal{N} = 4$ Super Yang Mills Theory, orbifolded by $\\mathbb{Z}_3$, which mimics the behaviour of a dimensionally reduced $\\mathcal{N} = 1$, 10-dimensional gauge theory over a set of fuzzy spheres at intermediate high scales and leads to the trinification GUT $SU(3)^3$ at slightly lower, which in turn can be spontaneously broken to the MSSM in low scales.
Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions
Lapidus, Michel L; Žubrinić, Darko
2017-01-01
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...
Emission of massive scalar fields by a higher-dimensional rotating black hole
International Nuclear Information System (INIS)
Kanti, P.; Pappas, N.
2010-01-01
We perform a comprehensive study of the emission of massive scalar fields by a higher-dimensional, simply rotating black hole both in the bulk and on the brane. We derive approximate, analytic results as well as exact numerical ones for the absorption probability, and demonstrate that the two sets agree very well in the low and intermediate-energy regime for scalar fields with mass m Φ ≤1 TeV in the bulk and m Φ ≤0.5 TeV on the brane. The numerical values of the absorption probability are then used to derive the Hawking radiation power emission spectra in terms of the number of extra dimensions, angular-momentum of the black hole and mass of the emitted field. We compute the total emissivities in the bulk and on the brane, and demonstrate that, although the brane channel remains the dominant one, the bulk-over-brane energy ratio is considerably increased (up to 34%) when the mass of the emitted field is taken into account.
What we think about the higher dimensional Chern-Simons theories
International Nuclear Information System (INIS)
Fock, V.V.; Nekrasov, N.A.; Rosly, A.A.; Selivanov, K.G.
1992-01-01
This paper reports that one of the most interesting developments in mathematical physics was the investigation of the so-called topological field theories i.e. such theories which do not need a metric on the manifold for their definition a d hence the observable of which are topologically invariant. The Chern-Simons (CS) functionals considered as actions give us examples the theories of such a type. The CS theory on a 3d manifold was firstly considered in the Abelian case by A.S. Schwartz and then after papers of E. Witten there has been an explosive process of publications on this subject. This paper discusses topological invariants of the manifolds (like the Ray-Singer torsion) computed by the quantum field theory methods; conformal blocks of 2d conformal field theories as vectors in the CS theory Hilbert space; correlators of Wilson loop and the invariants of 1d links in 3d manifolds; braid groups; unusual relations between spin and statistics; here we would like to consider the generalization of a part of the outlined ideas to the CS theories on higher dimensional manifolds. Some of our results intersect with
Partially-massless higher-spin algebras and their finite-dimensional truncations
International Nuclear Information System (INIS)
Joung, Euihun; Mkrtchyan, Karapet
2016-01-01
The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS d+1 are studied. The algebras involving PM generators up to depth 2 (ℓ−1) are defined as the maximal symmetries of free conformal scalar field with 2 ℓ order wave equation in d dimensions. We review the construction of these algebras by quotienting certain ideals in the universal enveloping algebra of (A)dS d+1 isometries. We discuss another description in terms of Howe duality and derive the formula for computing trace in these algebras. This enables us to explicitly calculate the bilinear form for this one-parameter family of algebras. In particular, the bilinear form shows the appearance of additional ideal for any non-negative integer values of ℓ−d/2 , which coincides with the annihilator of the one-row ℓ-box Young diagram representation of so d+2 . Hence, the corresponding finite-dimensional coset algebra spanned by massless and PM generators is equivalent to the symmetries of this representation.
Anderson, Daniel M.; McLaughlin, Richard M.; Miller, Cass T.
2018-02-01
We examine a mathematical model of one-dimensional draining of a fluid through a periodically-layered porous medium. A porous medium, initially saturated with a fluid of a high density is assumed to drain out the bottom of the porous medium with a second lighter fluid replacing the draining fluid. We assume that the draining layer is sufficiently dense that the dynamics of the lighter fluid can be neglected with respect to the dynamics of the heavier draining fluid and that the height of the draining fluid, represented as a free boundary in the model, evolves in time. In this context, we neglect interfacial tension effects at the boundary between the two fluids. We show that this problem admits an exact solution. Our primary objective is to develop a homogenization theory in which we find not only leading-order, or effective, trends but also capture higher-order corrections to these effective draining rates. The approximate solution obtained by this homogenization theory is compared to the exact solution for two cases: (1) the permeability of the porous medium varies smoothly but rapidly and (2) the permeability varies as a piecewise constant function representing discrete layers of alternating high/low permeability. In both cases we are able to show that the corrections in the homogenization theory accurately predict the position of the free boundary moving through the porous medium.
Perturbative Critical Behavior from Spacetime Dependent Couplings
International Nuclear Information System (INIS)
Torroba, Gonzalo
2012-01-01
We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-ε Wilson-Fisher fixed point. Rather than considering 4-ε dimensions, we stay in four dimensions but introduce couplings whose leading spacetime dependence is of the form λx κ μ κ , with a small parameter κ playing a role analogous to ε. We show, in φ 4 theory and in QED and QCD with massless flavors, that this leads to a critical theory under perturbative control over an exponentially wide window of spacetime positions x. The exact fixed point coupling λ * (x) in our theory is identical to the running coupling of the translationally invariant theory, with the scale replaced by 1/x. Similar statements hold for three-dimensional φ 6 theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.
International Nuclear Information System (INIS)
Nabbi, R.; Meister, G.; Finken, R.; Haben, M.
1982-09-01
The present report describes the modelling basis and the structure of the neutron kinetics-code SHOVAV-Juel. Information for users is given regarding the application of the code and the generation of the input data. SHOVAV-Juel is a one-dimensional space-time-code based on a multigroup diffusion approach for four energy groups and six groups of delayed neutrons. It has been developed for the analysis of the transient behaviour of high temperature reactors with pebble-bed core. The reactor core is modelled by horizontal segments to which different materials compositions can be assigned. The temperature dependence of the reactivity is taken into account by using temperature dependent neutron cross sections. For the simulation of transients in an extended time range the time dependence of the reactivity absorption by Xenon-135 is taken into account. (orig./RW)
Directory of Open Access Journals (Sweden)
Hasibun Naher
2012-01-01
Full Text Available We construct new analytical solutions of the (3+1-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.
Schrödinger, Erwin
1985-01-01
In response to repeated requests this classic book on space-time structure by Professor Erwin Schrödinger is now available in the Cambridge Science Classics series. First published in 1950, and reprinted in 1954 and 1960, this lucid and profound exposition of Einstein's 1915 theory of gravitation still provides valuable reading for students and research workers in the field.
Gauged supergravities in various spacetime dimensions
Energy Technology Data Exchange (ETDEWEB)
Weidner, M.
2006-12-15
In this thesis we study the gaugings of extended supergravity theories in various space-time dimensions. These theories describe the low-energy limit of non-trivial string compactifications. For each theory under consideration we work out all possible gaugings that are compatible with supersymmetry. They are parameterized by the so-called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half-maximal (N=4) supergravities in d=4 and d=5 and to the maximal supergravities in d=2 and d=7. Examples of particular gaugings are given. Whenever possible, the higher-dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor. (orig.)
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.; Salama, Khaled N.
2010-01-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.
2010-06-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
Energy Technology Data Exchange (ETDEWEB)
Pfeifer, Christian
2013-11-15
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
International Nuclear Information System (INIS)
Pfeifer, Christian
2013-11-01
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
Operational definition of (brane-induced) space-time and constraints on the fundamental parameters
International Nuclear Information System (INIS)
Maziashvili, Michael
2008-01-01
First we contemplate the operational definition of space-time in four dimensions in light of basic principles of quantum mechanics and general relativity and consider some of its phenomenological consequences. The quantum gravitational fluctuations of the background metric that comes through the operational definition of space-time are controlled by the Planck scale and are therefore strongly suppressed. Then we extend our analysis to the braneworld setup with low fundamental scale of gravity. It is observed that in this case the quantum gravitational fluctuations on the brane may become unacceptably large. The magnification of fluctuations is not linked directly to the low quantum gravity scale but rather to the higher-dimensional modification of Newton's inverse square law at relatively large distances. For models with compact extra dimensions the shape modulus of extra space can be used as a most natural and safe stabilization mechanism against these fluctuations
Bi-conformal symmetry and static Green functions in the Schwarzschild-Tangherlini spacetimes
International Nuclear Information System (INIS)
Frolov, Valeri P.; Zelnikov, Andrei
2015-01-01
We study a static massless minimally coupled scalar field created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for this field is invariant under a special transformation of the background metric. This transformation consists of the static conformal transformation of the spatial part of the metric accompanied by a properly chosen transformation of the red-shift factor. Both transformations are determined by one function Ω of the spatial coordinates. We show that in a case of higher dimensional spherically symmetric black holes one can find such a bi-conformal transformation that the symmetry of the D-dimensional metric is enhanced after its application. Namely, the metric becomes a direct sum of the metric on a unit sphere and the metric of 2D anti-de Sitter space. The method of the heat kernels is used to find the Green function in this new space, which allows one, after dimensional reduction, to obtain a static Green function in the original space of the static black hole. The general useful representation of static Green functions is obtained in the Schwarzschild-Tangherlini spacetimes of arbitrary dimension. The exact explicit expressions for the static Green functions are obtained in such metrics for D<6. It is shown that in the four dimensional case the corresponding Green function coincides with the Copson solution.
International Nuclear Information System (INIS)
Villasenor, R.F.; Bonilla, J.L.L.; Zuniga, G.O.; Matos, T.
1989-01-01
The authors study space-times embedded in E 5 (that means, pseudo-euclidean five-dimensional spaces) in the intrinsic rigidity case, i.e., when the second fundamental form b if can be determined by the internal geometry of the four-dimensional Riemannian space R 4 . They write down the Gauss and Codazzi equations determining the local isometric embedding of R 4 in E 5 and give some consequences of it. They prove that when there exists intrinsic rigidity, then b if is a linear combination of the metric and Ricci tensor; it is given some applications for the de Sitter and Einstein models
Lohe, M. A.
2018-06-01
We generalize the Watanabe–Strogatz (WS) transform, which acts on the Kuramoto model in d = 2 dimensions, to a higher-dimensional vector transform which operates on vector oscillator models of synchronization in any dimension , for the case of identical frequency matrices. These models have conserved quantities constructed from the cross ratios of inner products of the vector variables, which are invariant under the vector transform, and have trajectories which lie on the unit sphere S d‑1. Application of the vector transform leads to a partial integration of the equations of motion, leaving independent equations to be solved, for any number of nodes N. We discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on S d‑1. We further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball , and leaves invariant the cross ratios constructed from inner products of vectors in . This mapping can be used to partially integrate a system of vector oscillators with trajectories in , and for d = 2 leads to an extension of the Kuramoto system to a system of oscillators with time-dependent amplitudes and trajectories in the unit disk. We find an inequivalent generalization of the Möbius map which also preserves but leaves invariant a different set of cross ratios, this time constructed from the vector norms. This leads to a different extension of the Kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations.
A higher-dimensional Bianchi type-I inflationary Universe in general ...
Indian Academy of Sciences (India)
Inflation, the stage of accelerated expansion of the Universe, first proposed ... ary model in the context of grand unified theory (GUT), which has been ... The role of self-interacting scalar fields in inflationary cosmology in four-dimensional.
First law of black ring thermodynamics in higher dimensional Chern-Simons gravity
International Nuclear Information System (INIS)
Rogatko, Marek
2007-01-01
The physical process version and the equilibrium state version of the first law of black ring thermodynamics in n-dimensional Einstein gravity with Chern-Simons term were derived. This theory constitutes the simplest generalization of the five-dimensional one admitting a stationary black ring solution. The equilibrium state version of the first law of black ring mechanics was achieved by choosing any cross section of the event horizon to the future of the bifurcation surface
International Nuclear Information System (INIS)
Taghavi-Chabert, Arman
2011-01-01
Optical (or Robinson) structures are one generalization of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg-Sachs theorem to five dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalizes the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor. This results in a significant simplification of the field equations. We discuss possible degenerate cases, including a five-dimensional generalization of the Petrov type D condition. We also show that the vacuum black ring solution is endowed with optical structures, yet fails to be algebraically special with respect to them. We finally explain the generalization of these ideas to higher dimensions, which has been checked in six and seven dimensions.
The inverse spatial Laplacian of spherically symmetric spacetimes
International Nuclear Information System (INIS)
Fernandes, Karan; Lahiri, Amitabha
2017-01-01
We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field. (paper)
Energy Technology Data Exchange (ETDEWEB)
Racz, Istvan, E-mail: iracz@rmki.kfki.h [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)
2010-08-07
The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by {gamma} one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime (M, g{sub ab}). First, it is shown that it is always possible to select a synchronized family of causal geodesics {Gamma} and an open neighbourhood U of a final segment of {gamma} in M such that U comprises members of {Gamma}, and suitable local coordinates can be defined everywhere on U provided that {gamma} does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime (M, g{sub ab}) is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order k - 1 are bounded on U, and also the line integrals of the components of the kth-order covariant derivatives are finite along the members of {Gamma}-where all the components are meant to be registered with respect to a synchronized frame field on U-then there exists a C{sup k-} extension {Phi} : (M,g{sub ab}) {yields}(M,g{sub ab}) so that for each {gamma}-bar from {Gamma}, which is inextendible in (M, g{sub ab}), the image, {Phi}{gamma}-bar, is extendible in (M,g{sub ab}). Finally, it is also proved that whenever {gamma} does terminate on a topological singularity (M, g{sub ab}) cannot be generic.
Hong, Sungwoo
Warped higher-dimensional compactifications with "bulk'' standard model, or their AdS/CFT dual as the purely 4D scenario of Higgs compositeness and partial compositeness, offer an elegant approach to resolving the electroweak hierarchy problem as well as the origins of flavor structure. However, low-energy electroweak/flavor/CP constraints and the absence of non-standard physics at LHC Run 1 suggest that a "little hierarchy problem'' remains, and that the new physics underlying naturalness may lie out of LHC reach. Assuming this to be the case, we show that there is a simple and natural extension of the minimal warped model in the Randall-Sundrum framework, in which matter, gauge and gravitational fields propagate modestly different degrees into the IR of the warped dimension, resulting in rich and striking consequences for the LHC (and beyond). The LHC-accessible part of the new physics is AdS/CFT dual to the mechanism of "vectorlike confinement'', with TeV-scale Kaluza-Klein excitations of the gauge and gravitational fields dual to spin-0,1,2 composites. Unlike the minimal warped model, these low-lying excitations have predominantly flavor-blind and flavor/CP-safe interactions with the standard model. In addition, the usual leading decay modes of the lightest KK gauge bosons into top and Higgs bosons are suppressed. This effect permits erstwhile subdominant channels to become significant. These include flavor-universal decays to all pairs of SM fermions, and a novel channel--decay to a radion and a SM gauge boson, followed by radion decay to a pair of SM gauge bosons. We present a detailed phenomenological study of the latter cascade decay processes. Remarkably, this scenario also predicts small deviations from flavor-blindness originating from virtual effects of Higgs/top compositeness at O(10) TeV, with subdominant resonance decays into a pair of Higgs/top-rich final states, giving the LHC an early "preview'' of the nature of the resolution of the hierarchy
Topology of classical vacuum space-time
International Nuclear Information System (INIS)
Cho, Y.M.
2007-04-01
We present a topological classification of classical vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology π 3 (S 3 ) = π 3 (S 2 ). Viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that the vacuum connection has the knot topology, the same topology which describes the multiple vacua of SU(2) gauge theory. We discuss the physical implications of our result in quantum gravity. (author)
Petrov classification and holographic reconstruction of spacetime
Energy Technology Data Exchange (ETDEWEB)
Gath, Jakob [Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR 7644,91128 Palaiseau Cedex (France); Mukhopadhyay, Ayan [Department of Physics, University of Crete,Heraklion 71003 (Greece); Petkou, Anastasios C. [Department of Physics, Institute of Theoretical Physics,Aristotle University of Thessaloniki,54124, Thessaloniki (Greece); Petropoulos, P. Marios [Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR 7644,91128 Palaiseau Cedex (France); Siampos, Konstantinos [Albert Einstein Center for Fundamental Physics,Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-09-01
Using the asymptotic form of the bulk Weyl tensor, we present an explicit approach that allows us to reconstruct exact four-dimensional Einstein spacetimes which are algebraically special with respect to Petrov’s classification. If the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless, then the bulk metric is exactly resummed and captures modes that stand beyond the hydrodynamic derivative expansion. We illustrate the method when the congruence has zero vorticity, leading to the Robinson-Trautman spacetimes of arbitrary Petrov class, and quote the case of non-vanishing vorticity, which captures the Plebański-Demiański Petrov D family.
International Nuclear Information System (INIS)
Wiliardy, Abednego; Gunara, Bobby Eka
2016-01-01
An n dimensional flat manifold N is embedded into an n +1 dimensional stationary manifold M. The metric of M is derived from a general form of stationary manifold. By taking several assumption, such as 1) the ambient manifold M to be maximally symmetric space and satisfying a pure gauge condition, and 2) the submanifold is taken to be flat, then we find the solution that satisfies Ricci scalar of N . Moreover, we determine whether the solution is compatible with the Ricci and Riemann tensor of manifold N depending on the dimension. (paper)
Fourier two-level analysis for higher dimensional discontinuous Galerkin discretisation
P.W. Hemker (Piet); M.H. van Raalte (Marc)
2002-01-01
textabstractIn this paper we study the convergence of a multigrid method for the solution of a two-dimensional linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods. For the Baumann-Oden and for the symmetric DG method, we give a detailed analysis of the
Faster exact algorithms for computing Steiner trees in higher dimensional Euclidean spaces
DEFF Research Database (Denmark)
Fonseca, Rasmus; Brazil, Marcus; Winter, Pawel
The Euclidean Steiner tree problem asks for a network of minimum total length interconnecting a finite set of points in d-dimensional space. For d ≥ 3, only one practical algorithmic approach exists for this problem --- proposed by Smith in 1992. A number of refinements of Smith's algorithm have...
Dimensional reduction of 10d heterotic string effective lagrangian with higher derivative terms
International Nuclear Information System (INIS)
Lalak, Z.; Pawelczyk, J.
1989-11-01
Dimensional reduction of the 10d Supergravity-Yang-Mills theories containing up to four derivatives is described. Unexpected nondiagonal corrections to 4d gauge kinetic function and negative contributions to scalar potential are found. We analyzed the general structure of the resulting lagrangian and discuss the possible phenomenological consequences. (author)
Uniqueness in some higher order elliptic boundary value problems in n dimensional domains
Directory of Open Access Journals (Sweden)
C.-P. Danet
2011-07-01
Full Text Available We develop maximum principles for several P functions which are defined on solutions to equations of fourth and sixth order (including a equation which arises in plate theory and bending of cylindrical shells. As a consequence, we obtain uniqueness results for fourth and sixth order boundary value problems in arbitrary n dimensional domains.
Testud, Frederik; Gallichan, Daniel; Layton, Kelvin J; Barmet, Christoph; Welz, Anna M; Dewdney, Andrew; Cocosco, Chris A; Pruessmann, Klaas P; Hennig, Jürgen; Zaitsev, Maxim
2015-03-01
PatLoc (Parallel Imaging Technique using Localized Gradients) accelerates imaging and introduces a resolution variation across the field-of-view. Higher-dimensional encoding employs more spatial encoding magnetic fields (SEMs) than the corresponding image dimensionality requires, e.g. by applying two quadratic and two linear spatial encoding magnetic fields to reconstruct a 2D image. Images acquired with higher-dimensional single-shot trajectories can exhibit strong artifacts and geometric distortions. In this work, the source of these artifacts is analyzed and a reliable correction strategy is derived. A dynamic field camera was built for encoding field calibration. Concomitant fields of linear and nonlinear spatial encoding magnetic fields were analyzed. A combined basis consisting of spherical harmonics and concomitant terms was proposed and used for encoding field calibration and image reconstruction. A good agreement between the analytical solution for the concomitant fields and the magnetic field simulations of the custom-built PatLoc SEM coil was observed. Substantial image quality improvements were obtained using a dynamic field camera for encoding field calibration combined with the proposed combined basis. The importance of trajectory calibration for single-shot higher-dimensional encoding is demonstrated using the combined basis including spherical harmonics and concomitant terms, which treats the concomitant fields as an integral part of the encoding. © 2014 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Peng Junjin; Wu Shuangqing
2008-01-01
Motivated by the success of the recently proposed method of anomaly cancellation to derive Hawking fluxes from black hole horizons of spacetimes in various dimensions, we have further extended the covariant anomaly cancellation method shortly simplified by Banerjee and Kulkarni to explore the Hawking radiation of the (3+1)-dimensional charged rotating black strings and their higher dimensional extensions in anti-de Sitter spacetimes, whose horizons are not spherical but can be toroidal, cylindrical or planar, according to their global identifications. It should be emphasized that our analysis presented here is very general in the sense that the determinant of the reduced (1+1)-dimensional effective metric from these black strings need not be equal to one (√(-g)≠1). Our results indicate that the gauge and energy-momentum fluxes needed to cancel the (1+1)-dimensional covariant gauge and gravitational anomalies are compatible with the Hawking fluxes. Besides, thermodynamics of these black strings are studied in the case of a variable cosmological constant
Explicit Minkowski invariance and differential calculus in the quantum space-time
International Nuclear Information System (INIS)
Xu Zhan.
1991-11-01
In terms of the R-circumflex matrix of the quantum group SL q (2), the explicit Minkowski coordinate commutation relations in the four-dimensional quantum space-time are given, and the invariance of the Minkowski metric is shown. The differential calculus in this quantum space-time is discussed and the corresponding commutation relations are proposed. (author). 17 refs
International Nuclear Information System (INIS)
Kuetche, Victor Kamgang; Bouetou, Thomas Bouetou; Kofane, Timoleon Crepin
2010-12-01
We investigate the singularity structure analysis of the higher-dimensional time-gated Manakov system referring to the (2+1)-dimensional coupled nonlinear Schroedinger (CNLS) equations, and we show that these equations are Painleve-integrable. By means of the Weiss et al.'s methodology, we show the arbitrariness of the expansion coefficients and the consistency of the truncation corresponding to a special Baecklund transformation (BT) of these CNLS equations. In the wake of such transformation, following the Hirota's formalism, we derive a one-soliton solution. Besides, by using the Zakharov-Shabat (ZS) scheme which provides a general Lax-representation of an evolution system, we show that the (2+1)-dimensional CNLS system under interests is completely integrable. Furthermore, using the arbitrariness of the above coefficients, we unearth and investigate a typical spectrum of periodic coherent structures while depicting elastic interactions amongst such patterns. (author)
Temperature and entropy of Schwarzschild-de Sitter space-time
International Nuclear Information System (INIS)
Shankaranarayanan, S.
2003-01-01
In the light of recent interest in quantum gravity in de Sitter space, we investigate semiclassical aspects of four-dimensional Schwarzschild-de Sitter space-time using the method of complex paths. The standard semiclassical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild-de Sitter space-time or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity--the inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild-de Sitter space-time, we apply the method of complex paths to three different coordinate systems--spherically symmetric, Painleve, and Lemaitre. We show that the equilibrium temperature in Schwarzschild-de Sitter space-time is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons, analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild-de Sitter space-time satisfies the D-bound conjecture
Maximal locality and predictive power in higher-dimensional, compactified field theories
International Nuclear Information System (INIS)
Kubo, Jisuke; Nunami, Masanori
2004-01-01
To realize maximal locality in a trivial field theory, we maximize the ultraviolet cutoff of the theory by fine tuning the infrared values of the parameters. This optimization procedure is applied to the scalar theory in D + 1 dimensional (D ≥ 4) with one extra dimension compactified on a circle of radius R. The optimized, infrared values of the parameters are then compared with the corresponding ones of the uncompactified theory in D dimensions, which is assumed to be the low-energy effective theory. We find that these values approximately agree with each other as long as R -1 > approx sM is satisfied, where s ≅ 10, 50, 50, 100 for D = 4,5,6,7, and M is a typical scale of the D-dimensional theory. This result supports the previously made claim that the maximization of the ultraviolet cutoff in a nonrenormalizable field theory can give the theory more predictive power. (author)
Higher conservation laws for ten-dimensional supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Abdalla, E.; Forger, M.; Freiburg Univ.; Jacques, M.
1988-01-01
It is shown that ten-dimensional supersymmetric Yang-Mills theories are integrable systems, in the (weak) sense of admitting a (superspace) Lax representation for their equations of motion. This is achieved by means of an explicit proof that the equations of motion are not only a consequence of but in fact fully equivalent to the superspace constraint F αβ =0. Moreover, a procedure for deriving infinite series of non-local conservation laws is outlined. (orig.)
The classification of static plane-symmetric spacetimes
International Nuclear Information System (INIS)
Ziad, M.
1999-01-01
According to the classical literature, here a complete classification of static plane-symmetric spacetimes according to their isometries and metrics is provided,without imposing any restriction on the stress-energy tensor. It turns out that these spacetimes admit G r as the maximal isometry groups whereas their Killing vector fields are obtained. The Einstein field equations are used to discuss the stress energy tensors of the spacetimes admitting higher symmetries along with their Segre' and Plebanski types and finally results are compared with those of Taub, Hall and Steele
Knotty inflation and the dimensionality of spacetime
Energy Technology Data Exchange (ETDEWEB)
Berera, Arjun [University of Edinburgh, Tait Institute, School of Physics and Astronomy, Edinburgh (United Kingdom); Buniy, Roman V. [Chapman University, Schmid College of Science, Orange, CA (United States); Kephart, Thomas W. [Vanderbilt University, Department of Physics and Astronomy, Nashville, TN (United States); Paes, Heinrich [Technische Universitaet Dortmund, Fakultaet fuer Physik, Dortmund (Germany); Rosa, Joao G. [Departamento de Fisica da Universidade de Aveiro and CIDMA, Aveiro (Portugal)
2017-10-15
We suggest a structure for the vacuum comprised of a network of tightly knotted/linked flux tubes formed in a QCD-like cosmological phase transition and show that such a network can drive cosmological inflation. As the network can be topologically stable only in three space dimensions, this scenario provides a dynamical explanation for the existence of exactly three large spatial dimensions in our Universe. (orig.)
Global structure of spacetimes
International Nuclear Information System (INIS)
Geroch, R.; Horowitz, G.T.
1979-01-01
An extended introduction is followed by a section entitled: 'what is the topology of our universe', in which such topics are considered as the underlying manifold, the qualitative behaviour of the light-cones, causal structure, and determinism. In the next section - 'is our universe singular', the famous singularity theorems are discussed. Finally, under 'how noticeably singular is our universe', the issue of cosmic censorship is discussed, i.e. that of whether or not one expects in certain circumstances that surviving observers will be able to detect singular behaviour in spacetime. (U.K.)
Why we observe an almost classical spacetime
Rosales, Jose-Luis; Sanchez-Gomez, Jose-Luis
1997-01-01
We argue that, in order to obtain decoherence of spacetime, we should consider quantum conformal metric fluctuations of spacetime. This could be the required environment in the problem of selfmeasurement of spacetime in quantum gravity.
On ``minimally curved spacetimes'' in general relativity
Dadhich, Naresh
1997-01-01
We consider a spacetime corresponding to uniform relativistic potential analogus to Newtonian potential as an example of ``minimally curved spacetime''. We also consider a radially symmetric analogue of the Rindler spacetime of uniform proper acceleration relative to infinity.
Quantum field in η-ξ spacetime
International Nuclear Information System (INIS)
Gui, Y.
1990-01-01
A new spacetime, η-ξ spacetime, is constructed. The quantum field in η-ξ spacetime is discussed. It is shown that the vacuum state of quantum field in η-ξ spacetime is a thermal state for an inertial observer in Minkowski spacetime, and the vacuum Green's functions in η-ξ spacetime are just the thermal Green's functions in usual statistical mechanics
Temporal and spatial foliations of spacetimes.
Herold, H.
For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.
Approaches to analysis of data that concentrate near higher-dimensional manifolds
International Nuclear Information System (INIS)
Friedman, J.H.; Tukey, J.W.; Tukey, P.A.
1979-01-01
The need to explore structure in high-dimensional clouds of data points that may concentrate near (possibly nonlinear) manifolds of lower dimension led to the current development of three new approaches. The first is a computer-graphic system (PRIM'79) that facilitates interactive viewing and manipulation of an ensemble of points. The other two are automatic procedures for separating a cloud into more manageable pieces. One of these (BIDEC) performs successive partitioning of the cloud by use of hyperplanes; the other (Cake Maker) explores expanding sequences of neighborhoods. Both procedures provide facilities for examining the resulting pieces and the relationships among them
Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime
International Nuclear Information System (INIS)
Middleton, Chad A.; Stanley, Ethan
2011-01-01
We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations in the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.
Natário, José; Queimada, Leonel; Vicente, Rodrigo
2018-04-01
We rederive the equations of motion for relativistic strings, that is, one-dimensional elastic bodies whose internal energy depends only on their stretching, and use them to study circular string loops rotating in the equatorial plane of flat and black hole spacetimes. We start by obtaining the conditions for equilibrium, and find that: (i) if the string’s longitudinal speed of sound does not exceed the speed of light then its radius when rotating in Minkowski’s spacetime is always larger than its radius when at rest; (ii) in Minkowski’s spacetime, equilibria are linearly stable for rotation speeds below a certain threshold, higher than the string’s longitudinal speed of sound, and linearly unstable for some rotation speeds above it; (iii) equilibria are always linearly unstable in Schwarzschild’s spacetime. Moreover, we study interactions of a rotating string loop with a Kerr black hole, namely in the context of the weak cosmic censorship conjecture and the Penrose process. We find that: (i) elastic string loops that satisfy the null energy condition cannot overspin extremal black holes; (ii) elastic string loops that satisfy the dominant energy condition cannot increase the maximum efficiency of the usual particle Penrose process; (iii) if the dominant energy condition (but not the weak energy condition) is violated then the efficiency can be increased. This last result hints at the interesting possibility that the dominant energy condition may underlie the well known upper bounds for the efficiencies of energy extraction processes (including, for example, superradiance).
On the quantization of spacetime
International Nuclear Information System (INIS)
Banai, M.
1981-01-01
A program of quantization of relativistic local field theories in terms of Hilbert modules over non-commutative Csup*-algebras is outlined. The spacetime of the considered systems should become a ''quantum'' represented by a Hilbert space. Two suggestions are given for the possible determination this quantum spacetime. (author)
Dimensional cosmological principles
International Nuclear Information System (INIS)
Chi, L.K.
1985-01-01
The dimensional cosmological principles proposed by Wesson require that the density, pressure, and mass of cosmological models be functions of the dimensionless variables which are themselves combinations of the gravitational constant, the speed of light, and the spacetime coordinates. The space coordinate is not the comoving coordinate. In this paper, the dimensional cosmological principle and the dimensional perfect cosmological principle are reformulated by using the comoving coordinate. The dimensional perfect cosmological principle is further modified to allow the possibility that mass creation may occur. Self-similar spacetimes are found to be models obeying the new dimensional cosmological principle
Classification of supersymmetric spacetimes in eleven dimensions
International Nuclear Information System (INIS)
Cariglia, Marco; Mac Conamhna, Oisin A.P.
2005-01-01
We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of 11-dimensional supergravity. The metric, four-form, and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four-form field equation to ensure that the solution of the Killing spinor equation also satisfies all the field equations, and we give these conditions explicitly
International Nuclear Information System (INIS)
Bombelli, L.; Lee, J.; Meyer, D.; Sorkin, R.D.
1987-01-01
We propose that space-time at the smallest scales is in reality a causal set: a locally finite set of elements endowed with a partial order corresponding to the macroscopic relation that defines past and future. We explore how a Lorentzian manifold can approximate a causal set, noting in particular that the thereby defined effective dimensionality of a given causal set can vary with length scale. Finally, we speculate briefly on the quantum dynamics of causal sets, indicating why an appropriate choice of action can reproduce general relativity in the classical limit
The wave equation on a curved space-time
International Nuclear Information System (INIS)
Friedlander, F.G.
1975-01-01
It is stated that chapters on differential geometry, distribution theory, and characteristics and the propagation of discontinuities are preparatory. The main matter is in three chapters, entitled: fundamental solutions, representation theorems, and wave equations on n-dimensional space-times. These deal with general construction of fundamental solutions and their application to the Cauchy problem. (U.K.)
Partially ordered sets, transfinite topology and the dimension of Cantorian-fractal spacetime
Energy Technology Data Exchange (ETDEWEB)
Marek-Crnjac, L. [Institute of Mathematics and Physics, University of Maribor (Slovenia)], E-mail: leila.marek@guest.arnes.si
2009-11-15
We introduce partially ordered sets and relate them to random Cantor sets of E-infinity theory. Subsequently we derive the dimensionality of Cantorian-fractal spacetime using posets and E-infinity transfinite Cantor sets.
Space-time neutronic analysis of postulated LOCA's in CANDU reactors
International Nuclear Information System (INIS)
Luxat, J.C.; Frescura, G.M.
1978-01-01
Space-time neutronic behaviour of CANDU reactors is of importance in the analysis and design of reactor safety systems. A methodology has been developed for simulating CANDU space-time neutronics with application to the analysis of postulated LOCA'S. The approach involves the efficient use of a set of computer codes which provide a capability to perform simulations ranging from detailed, accurate 3-dimensional space-time to low-cost survey calculations using point kinetics with some ''effective'' spatial content. A new, space-time kinetics code based upon a modal expansion approach is described. This code provides an inexpensive and relatively accurate scoping tool for detailed 3-dimensional space-time simulations. (author)
Higher first Chern numbers in one-dimensional Bose-Fermi mixtures
Knakkergaard Nielsen, Kristian; Wu, Zhigang; Bruun, G. M.
2018-02-01
We propose to use a one-dimensional system consisting of identical fermions in a periodically driven lattice immersed in a Bose gas, to realise topological superfluid phases with Chern numbers larger than 1. The bosons mediate an attractive induced interaction between the fermions, and we derive a simple formula to analyse the topological properties of the resulting pairing. When the coherence length of the bosons is large compared to the lattice spacing and there is a significant next-nearest neighbour hopping for the fermions, the system can realise a superfluid with Chern number ±2. We show that this phase is stable in a large region of the phase diagram as a function of the filling fraction of the fermions and the coherence length of the bosons. Cold atomic gases offer the possibility to realise the proposed system using well-known experimental techniques.
Black Hole Hair in Higher Dimensions
International Nuclear Information System (INIS)
Cao Chao; Chen Yixin; Li Jianlong
2010-01-01
We study the property of matter in equilibrium with a static, spherically symmetric black hole in D-dimensional spacetime. It requires that this kind of matter has an equation of state ω = p r /ρ = -n/(n + 2k), k, n epsilon N (where n > 1 corresponds to a mixture of vacuum matter and 'hair' matter), which seems to be independent of D. However, when we associate this result with specific models, we find that these hairy black holes can live only in some special dimensional spacetime: (i) D = 2 + 2k/n while the black hole is surrounded by cosmic strings, which requires D is even or D epsilon N, depending on the value of n, this is consistent with some important results in superstring theory, it might reveal the relation between cosmic string and superstring in another aspect; (ii) the black hole can be surrounded by linear dilaton field only in 4-dimensional spacetime. In both cases, D = 4 is special. We also present some examples of such hairy black holes in higher dimensions, including a toy model with negative energy density. (general)
Springer handbook of spacetime
Petkov, Vesselin
2014-01-01
The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Han...
International Nuclear Information System (INIS)
Hawking, S.
1989-01-01
This chapter answers some fundamental questions about the limits, spatial and temporal of the universe. The Big Bang and Big Crunch, the temporal end pieces of the universe are explained in terms of curved spacetime using Einstein's theory of general relativity and quantum mechanics. Evidence for the Big Bang including large scale uniformity and discovery of the microwave background radiation are explained. In defining the boundary conditions of the universe, it is suggested that there are no boundary conditions, i.e. that time ceases to be well defined in the very early universe. Thus discussion about events prior to the Big Bang cease to have any meaning. The model offers, as yet unexplained, predictive potential. (U.K.)
Polarized electrogowdy spacetimes censored
International Nuclear Information System (INIS)
Nungesser, Ernesto
2010-01-01
A sketch of the proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.
Polarized electrogowdy spacetimes censored
Energy Technology Data Exchange (ETDEWEB)
Nungesser, Ernesto, E-mail: ernesto.nungesser@aei.mpg.d [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany)
2010-05-01
A sketch of the proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.
International Nuclear Information System (INIS)
Abbagari, Souleymanou; Bouetou, Thomas B.; Kofane, Timoleon C.
2013-01-01
The prolongation structure methodologies of Wahlquist—Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Bäcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention. (general)
A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids
Energy Technology Data Exchange (ETDEWEB)
Bungartz, H.J. [Technische Universitaet Muenchen (Germany)
1996-12-31
In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.
Swimming versus swinging effects in spacetime
International Nuclear Information System (INIS)
Gueron, Eduardo; Maia, Clovis A. S.; Matsas, George E. A.
2006-01-01
Wisdom has recently unveiled a new relativistic effect, called 'spacetime swimming', where quasirigid free bodies in curved spacetimes can 'speed up', 'slow down' or 'deviate' their falls by performing local cyclic shape deformations. We show here that for fast enough cycles this effect dominates over a nonrelativistic related one, named here 'space swinging', where the fall is altered through nonlocal cyclic deformations in Newtonian gravitational fields. We expect, therefore, to clarify the distinction between both effects leaving no room to controversy. Moreover, the leading contribution to the swimming effect predicted by Wisdom is enriched with a higher order term and the whole result is generalized to be applicable in cases where the tripod is in large redshift regions
Topology and isometries of the de Sitter space-time
International Nuclear Information System (INIS)
Mitskevich, N.V.; Senin, Yu.E.
1982-01-01
Spaces with a constant four-dimensional curvature, which are locally isometric to the de Sitter space-time but differing from it in topology are considered. The de Sitter spaces are considered in coordinates fitted at best for introduction of topology for three cross sections: S 3 , S 1 x S 2 , S 1 x S 2 x S 3 . It is shown that the de Sitter space-time covered by the family of layers, each of them is topologically identical, may be covered by another family of topologically identical layers. But layers in these families will have different topology
On quantization of free fields in stationary space-times
International Nuclear Information System (INIS)
Moreno, C.
1977-01-01
In Section 1 the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections, is analysed, an existence and uniqueness theorem is given for the Lichnerowicz distribution kernel G 1 together with its proper Fourier expansion, and the Hilbert spaces of frequency-part solutions defined by means of G 1 are constructed. In Section 2 an analysis, a theorem and a construction similar to the above are formulated for the free real field spin 1, mass m>0, in one kind of static space-times. (Auth.)
Homothetic matter collineations of LRS Bianchi type I spacetimes
Hussain, Tahir; Rahim, Waqas
2017-12-01
A complete classification of locally rotationally symmetric (LRS) Bianchi type I spacetimes via homothetic matter collineations (HMCs) is presented. For non-degenerate energy-momentum tensor, a general form of the vector field generating HMCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 6-, 7-, 8-, 10- or 11-dimensional Lie algebra of HMCs. When the energy-momentum tensor is degenerate, two cases give 6 and 11 HMCs, while the remaining cases produce infinite number of HMCs. Some LRS Bianchi type I metrics are provided admitting HMCs.
The causal boundary of wave-type spacetimes
International Nuclear Information System (INIS)
Flores, J.L.; Sanchez, M.
2008-01-01
A complete and systematic approach to compute the causal boundary of wave-type spacetimes is carried out. The case of a 1-dimensional boundary is specially analyzed and its critical appearance in pp-wave type spacetimes is emphasized. In particular, the corresponding results obtained in the framework of the AdS/CFT correspondence for holography on the boundary, are reinterpreted and very widely generalized. Technically, a recent new definition of causal boundary is used and stressed. Moreover, a set of mathematical tools is introduced (analytical functional approach, Sturm-Liouville theory, Fermat-type arrival time, Busemann-type functions)
Gheorghiu, Tamara; Vacaru, Sergiu I
2014-01-01
We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity, GR, and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of fundamental geometric/ physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes can be with Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Our method can be extended to higher dimensions which simplifies some proofs for imbedded and nonholonomically constrained four dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3-8 spacetime coordinates. There are anal...
Classical gauge theories on the coadjoint orbits of infinite dimensional groups
International Nuclear Information System (INIS)
Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung
1991-01-01
We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Quantum field theory in curved spacetime and black hole thermodynamics
Wald, Robert M
1994-01-01
In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth. This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum f...
International Nuclear Information System (INIS)
Hall, M.L.; Davis, A.B.
2005-01-01
Accurate modeling of radiative energy transport through cloudy atmospheres is necessary for both climate modeling with GCMs (Global Climate Models) and remote sensing. Previous modeling efforts have taken advantage of extreme aspect ratios (cells that are very wide horizontally) by assuming a 1-D treatment vertically - the Independent Column Approximation (ICA). Recent attempts to resolve radiation transport through the clouds have drastically changed the aspect ratios of the cells, moving them closer to unity, such that the ICA model is no longer valid. We aim to provide a higher-fidelity atmospheric radiation transport model which increases accuracy while maintaining efficiency. To that end, this paper describes the development of an efficient 3-D-capable radiation code that can be easily integrated into cloud resolving models as an alternative to the resident 1-D model. Applications to test cases from the Intercomparison of 3-D Radiation Codes (I3RC) protocol are shown
No-horizon theorem for spacetimes with spacelike G{sub 1} isometry groups
Energy Technology Data Exchange (ETDEWEB)
Goncalves, Sergio M C V [Department of Physics, Yale University, New Haven, CT 06511 (United States)
2003-12-21
We consider four-dimensional spacetimes (M, g) which obey the Einstein equations G = T and admit a global spacelike G{sub 1} = R isometry group. By means of dimensional reduction and local analysis on the reduced (2 + 1) spacetime, we obtain a sufficient condition on T which guarantees that (M, g) cannot contain apparent horizons. Given any (3 + 1) spacetime with spacelike translational isometry, the no-horizon condition can be readily tested without the need for dimensional reduction. This provides thus a useful and encompassing apparent horizon test for G{sub 1}-symmetric spacetimes. We argue that this adds further evidence towards the validity of the hoop conjecture and signals possible (albeit arguably unlikely) violations of strong cosmic censorship.
Deformed Spacetime Geometrizing Interactions in Four and Five Dimensions
Cardone, Fabio
2007-01-01
This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. Such a formalism (Deformed Special Relativity, DSR) allows one to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense) to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational) Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism. The mathematical pr...
Towards a theory of spacetime theories
Schiemann, Gregor; Scholz, Erhard
2017-01-01
This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spaceti...
The phase structure of higher-dimensional black rings and black holes
International Nuclear Information System (INIS)
Emparan, Roberto; Harmark, Troels; Niarchos, Vasilis; Obers, Niels A.; RodrIguez, Maria J.
2007-01-01
We construct an approximate solution for an asymptotically flat, neutral, thin rotating black ring in any dimension D ≥ 5 by matching the near-horizon solution for a bent boosted black string, to a linearized gravity solution away from the horizon. The rotating black ring solution has a regular horizon of topology S 1 x S D-3 and incorporates the balancing condition of the ring as a zero-tension condition. For D = 5 our method reproduces the thin ring limit of the exact black ring solution. For D ≥ 6 we show that the black ring has a higher entropy than the Myers-Perry black hole in the ultra-spinning regime. By exploiting the correspondence between ultra-spinning black holes and black membranes on a two-torus, we take steps towards qualitatively completing the phase diagram of rotating blackfolds with a single angular momentum. We are led to propose a connection between MP black holes and black rings, and between MP black holes and black Saturns, through merger transitions involving two kinds of 'pinched' black holes. More generally, the analogy suggests an infinite number of pinched black holes of spherical topology leading to a complicated pattern of connections and mergers between phases
Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry
International Nuclear Information System (INIS)
Afshar, Hamid; Creutzig, Thomas; Grumiller, Daniel; Hikida, Yasuaki; Rønne, Peter B.
2014-01-01
We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov W_n"("2")-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n=2 and n=4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k+n=(n+1)/(n−1). At these points, the W_n"("2")-algebra is nothing but a compactified free boson. This family of W-algebras admits an ’t Hooft limit. Further, in the case of n=4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product.
Fundamental and higher two-dimensional resonance modes of an Alpine valley
Ermert, Laura; Poggi, Valerio; Burjánek, Jan; Fäh, Donat
2014-08-01
We investigated the sequence of 2-D resonance modes of the sediment fill of Rhône Valley, Southern Swiss Alps, a strongly overdeepened, glacially carved basin with a sediment fill reaching a thickness of up to 900 m. From synchronous array recordings of ambient vibrations at six locations between Martigny and Sion we were able to identify several resonance modes, in particular, previously unmeasured higher modes. Data processing was performed with frequency domain decomposition of the cross-spectral density matrices of the recordings and with time-frequency dependent polarization analysis. 2-D finite element modal analysis was performed to support the interpretation of processing results and to investigate mode shapes at depth. In addition, several models of realistic bedrock geometries and velocity structures could be used to qualitatively assess the sensitivity of mode shape and particle motion dip angle to subsurface properties. The variability of modal characteristics due to subsurface properties makes an interpretation of the modes purely from surface observations challenging. We conclude that while a wealth of information on subsurface structure is contained in the modal characteristics, a careful strategy for their interpretation is needed to retrieve this information.
Spherical dust collapse in higher dimensions
International Nuclear Information System (INIS)
Goswami, Rituparno; Joshi, Pankaj S.
2004-01-01
We consider here whether it is possible to recover cosmic censorship when a transition is made to higher-dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as the end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear, that, in a generic higher-dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher-dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes on the nature of the initial data from which the collapse develops is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse
International Nuclear Information System (INIS)
Anderson, Gregory W.; Blazek, Tomas
2005-01-01
E 6 is an attractive group for unification model building. However, the complexity of a rank 6 group makes it nontrivial to write down the structure of higher dimensional operators in an E 6 theory in terms of the states labeled by quantum numbers of the standard model gauge group. In this paper, we show the results of our computation of the Clebsch-Gordan coefficients for the products of the 27 with irreducible representations of higher dimensionality: 78, 351, 351 ' , 351, and 351 ' . Application of these results to E 6 model building involving higher dimensional operators is straightforward
Decoherence and disentanglement of qubits detecting scalar fields in an expanded spacetime
International Nuclear Information System (INIS)
Li, Yujie; Dai, Yue; Shi, Yu
2017-01-01
We consider Unruh-Wald qubit detector model adopted for the far future region of an exactly solvable 1 + 1 dimensional scalar field theory in a toy model of Robertson-Walker expanding spacetime. It is shown that the expansion of the spacetime in its history enhances the decoherence of the qubit coupled with a scalar field. Moreover, we consider two entangled qubits, each locally coupled with a scalar field. The expansion of the spacetime in its history degrades the entanglement between the qubits, and it can lead to entanglement's sudden death if the initial entanglement is small enough. The details depend on the parameters characterizing the expansion of the spacetime. This work, on a toy model, suggests that the history of the spacetime might be probed through the coherent and entanglement behavior of the future detectors of quantum fields. In the present toy model, the two cosmological parameters can be determined from the quantum informational quantities of the detectors. (orig.)
Space-time structure and the origin of physical law
International Nuclear Information System (INIS)
Green, M.A.
1980-01-01
In the first part of this theses the author adopts a traditional world view, with space-time a topologically simple geometrical manifold, matter being represented by smooth classical fields, and space a Riemannian submanifold of space-time. It is shown how to characterize the space-time geometry in terms of fields defined on three-dimensional space. Accepting a finite number of the fields induced on space as independent initial data, a procedure is given for constructing dynamical and constraint equations which will propagate these fields forward in time. When the initial data are restricted to include only the hypersurface metric and the extrinsic curvature, the resulting equations combine to form the Einstein gravitational field equations with the cosmological term. The synthesis of gravitational and quantum physics is approached by proposing that the objective world underlying the perceived world is a four-dimensional topological manifold w, with no physically significant field structure and an unconstrianed and complex global topology. Conventional space-time is then a topologically simple replacement manifold for w. A preliminary outline of the correspondence is presented, based on a similarity between a natural graphical representation of 2 and the Feynman graphs of quantum field theory
Gravitating multidefects from higher dimensions
Giovannini, Massimo
2007-01-01
Warped configurations admitting pairs of gravitating defects are analyzed. After devising a general method for the construction of multidefects, specific examples are presented in the case of higher-dimensional Einstein-Hilbert gravity. The obtained profiles describe diverse physical situations such as (topological) kink-antikink systems, pairs of non-topological solitons and bound configurations of a kink and of a non-topological soliton. In all the mentioned cases the geometry is always well behaved (all relevant curvature invariants are regular) and tends to five-dimensional anti-de Sitter space-time for large asymptotic values of the bulk coordinate. Particular classes of solutions can be generalized to the framework where the gravity part of the action includes, as a correction, the Euler-Gauss-Bonnet combination. After scrutinizing the structure of the zero modes, the obtained results are compared with conventional gravitating configurations containing a single topological defect.
Fermion fields in η-ξ spacetime
International Nuclear Information System (INIS)
Gui, Y.
1992-01-01
Fermion fields in η-ζ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in η-ζ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in η-ζ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in η-ζ spacetime originates from Lorentz transformation properties of the fields
Directory of Open Access Journals (Sweden)
Liu Yang
2007-10-01
Full Text Available By using coincidence degree theory of Mawhin, existence results for some higher order resonance multipoint boundary value problems with one dimensional p-Laplacian operator are obtained.
Vacuum polarization in curved spacetime
International Nuclear Information System (INIS)
Guy, R.W.
1979-01-01
A necessary step in the process of understanding the quantum theory of gravity is the calculation of the stress-energy tensor of quantized fields in curved space-times. The determination of the stress tensor, a formally divergent object, is made possible in this dissertation by utilizing the zeta-function method of regularization and renormalization. By employing this scheme's representation of the renormalized effective action functional, an expression of the stress tensor for a massless, conformally invariant scalar field, first given by DeWitt, is derived. The form of the renormalized stress tensor is first tested in various examples of flat space-times. It is shown to vanish in Minkowski space and to yield the accepted value of the energy density in the Casimir effect. Next, the stress tensor is calculated in two space-times of constant curvature, the Einstein universe and the deSitter universe, and the results are shown to agree with those given by an expression of the stress tensor that is valid in conformally flat space-times. This work culminates in the determination of the stress tensor on the horizon of a Schwarzschild black hole. This is accomplished by approximating the radial part of the eigen-functions and the metric in the vicinity of the horizon. The stress tensor at this level approximation is found to be pure trace. The approximated forms of the Schwarzschild metric describes a conformally flat space-time that possesses horizons
Energy Technology Data Exchange (ETDEWEB)
Lin Kai, E-mail: lk314159@126.co [Institute of Theoretical Physics, China West Normal University, NanChong, SiChuan 637002 (China); Yang Shuzheng, E-mail: szyangcwnu@126.co [Institute of Theoretical Physics, China West Normal University, NanChong, SiChuan 637002 (China)
2009-10-12
Applying the method beyond semiclassical approximation, fermion tunneling from higher-dimensional anti-de Sitter Schwarzschild black hole is researched. In our work, the 'tortoise' coordinate transformation is introduced to simplify Dirac equation, so that the equation proves that only the (r-t) sector is important to our research. Because we only need to study the (r-t) sector, the Dirac equation is decomposed into several pairs of equations spontaneously, and we then prove the components of wave functions are proportional to each other in every pair of equations. Therefore, the suitable action forms of the wave functions are obtained, and finally the correctional Hawking temperature and entropy can be determined via the method beyond semiclassical approximation.
Directory of Open Access Journals (Sweden)
Li-Chun Zhang
2013-03-01
Full Text Available Using the new global embedding approach we investigate Unruh/Hawking temperature of the 5-dimensional minimal gauged supergravity black hole with double rotating parameters in a general (1 + 1 space-time. Our results verify that views of Banerjee and Majhi, and extend this approach to a higher dimension situation.
Energy Technology Data Exchange (ETDEWEB)
Schmidt, R.
2007-03-15
The present work is addressed to defects and boundaries in quantum field theory considering the application to AdS/CFT correspondence. We examine interactions of fermions with spins localised on these boundaries. Therefore, an algebra method is emphasised adding reflection and transmission terms to the canonical quantisation prescription. This method has already been applied to bosons in two space-time dimensions before. We show the possibilities of such reflection-transmission algebras in two, three, and four dimensions. We compare with models of solid state physics as well as with the conformal field theory approach to the Kondo effect. Furthermore, we discuss ansatzes of extensions to lattice structures. (orig.)
Four-dimensional Yang-Mills theory, gauge invariant mass and fluctuating three-branes
International Nuclear Information System (INIS)
Niemi, Antti J; Slizovskiy, Sergey
2010-01-01
We are interested in a gauge invariant coupling between four-dimensional Yang-Mills field and a three-brane that can fluctuate into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional spacetime under the influence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge field in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector field that propagates in the original spacetime R 4 . The presence of the brane becomes entirely invisible, expect for the mass.
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
Aspects of space-time dualities
Giveon, Amit
1996-01-01
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling matrices. We interpret (some of) such dualities as the geometrical symmetries of compactified theories in higher dimensions. In particular, we consider compactifications of a (self-dual) 2-form in 6-D, and compactifications of a self-dual 4-form in 10-D. Relations with a self-dual superstring in 6-D and with the type IIB superstring are discussed.
Quantum mechanics on noncommutative spacetime
International Nuclear Information System (INIS)
Calmet, Xavier; Selvaggi, Michele
2006-01-01
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect
Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
Directory of Open Access Journals (Sweden)
James M Chappell
Full Text Available Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
Chappell, James M; Iqbal, Azhar; Iannella, Nicolangelo; Abbott, Derek
2012-01-01
Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
Revisiting Special Relativity: A Natural Algebraic Alternative to Minkowski Spacetime
Chappell, James M.; Iqbal, Azhar; Iannella, Nicolangelo; Abbott, Derek
2012-01-01
Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension , with the unit imaginary producing the correct spacetime distance , and the results of Einstein’s then recently developed theory of special relativity, thus providing an explanation for Einstein’s theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary , with the Clifford bivector for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis and . We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton’s scattering formula, and a simple formulation of Dirac’s and Maxwell’s equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane. PMID:23300566
Observable Zitterbewegung in curved spacetimes
Kobakhidze, Archil; Manning, Adrian; Tureanu, Anca
2016-06-01
Zitterbewegung, as it was originally described by Schrödinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining particle states results in a mixing of positive and negative frequency modes. We explicitly demonstrate that such a mixing is in fact necessary to obtain the correct classical value for a particle's velocity in a uniformly accelerated reference frame, whereas in cosmological spacetime a particle does indeed exhibit Zitterbewegung.
Observable Zitterbewegung in curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Kobakhidze, Archil, E-mail: archilk@physics.usyd.edu.au [ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW 2006 (Australia); Manning, Adrian, E-mail: a.manning@physics.usyd.edu.au [ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW 2006 (Australia); Tureanu, Anca, E-mail: anca.tureanu@helsinki.fi [Department of Physics, University of Helsinki, P.O. Box 64, 00014 Helsinki (Finland)
2016-06-10
Zitterbewegung, as it was originally described by Schrödinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining particle states results in a mixing of positive and negative frequency modes. We explicitly demonstrate that such a mixing is in fact necessary to obtain the correct classical value for a particle's velocity in a uniformly accelerated reference frame, whereas in cosmological spacetime a particle does indeed exhibit Zitterbewegung.
Stochastic space-time and quantum theory
International Nuclear Information System (INIS)
Frederick, C.
1976-01-01
Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment
A novel spacetime concept for describing electronic motion within a helium atom
Xu, Kunming
2007-01-01
Euclidean space and linear algebra do not characterize dynamic electronic orbitals satisfactorily for even the motion of both electrons in an inert helium atom cannot be defined in reasonable details. Here the author puts forward a novel two-dimensional spacetime model from scratch in the context of defining both electrons in a helium atom. Space and time are treated as two orthogonal, symmetric and complementary quantities under the atomic spacetime. Electronic motion observed the rule of di...
The Dirac equation in the Lobachevsky space-time
International Nuclear Information System (INIS)
Paramonov, D.V.; Paramonova, N.N.; Shavokhina, N.S.
2000-01-01
The product of the Lobachevsky space and the time axis is termed the Lobachevsky space-time. The Lobachevsky space is considered as a hyperboloid's sheet in the four-dimensional pseudo-Euclidean space. The Dirac-Fock-Ivanenko equation is reduced to the Dirac equation in two special forms by passing from Lame basis in the Lobachevsky space to the Cartesian basis in the enveloping pseudo-Euclidean space
Maxwell-Chern-Simons theory for curved spacetime backgrounds
International Nuclear Information System (INIS)
Kant, E.; Klinkhamer, F.R.
2005-01-01
We consider a modified version of four-dimensional electrodynamics, which has a photonic Chern-Simons-like term with spacelike background vector in the action. Light propagation in curved spacetime backgrounds is discussed using the geometrical-optics approximation. The corresponding light path is modified, which allows for new effects. In a Schwarzschild background, for example, there now exist stable bounded orbits of light rays and the two polarization modes of light rays in unbounded orbits can have different gravitational redshifts
On the differentiability of space-time
International Nuclear Information System (INIS)
Clarke, C.J.S.
1977-01-01
It is shown that the differentiability of a space-time is implied by that of its Riemann tensor, assuming a priori only boundedness of the first derivations of the metric. Consequently all the results on space-time singularities proved in earlier papers by the author hold true in C 2- space-times. (author)
Divergence, spacetime dimension and fractal structure
International Nuclear Information System (INIS)
Nakamura, Hiroshi
2000-01-01
With a Cantor spacetime in mind, we assume the dimension of spacetime to be slightly smaller than four. Within the framework of QED, this dimension can be determined by calculating Feynman diagrams. We infer that the dimension of spacetime may be influenced by holes in space. (author)
Energy Technology Data Exchange (ETDEWEB)
Akbar, M.M., E-mail: akbar@utdallas.edu
2017-06-10
It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè–Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè–Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.
Jing, Yindi
2014-01-01
Distributed Space-Time Coding (DSTC) is a cooperative relaying scheme that enables high reliability in wireless networks. This brief presents the basic concept of DSTC, its achievable performance, generalizations, code design, and differential use. Recent results on training design and channel estimation for DSTC and the performance of training-based DSTC are also discussed.
Spacetimes foliated by Killing horizons
International Nuclear Information System (INIS)
Pawlowski, Tomasz; Lewandowski, Jerzy; Jezierski, Jacek
2004-01-01
It seems to be expected that a horizon of a quasi-local type, such as a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighbourhood in the spacetime, provided the vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so-called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by so-called non-expanding horizons. The obstacle is Kundt's constraint induced at the surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt's constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein-Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometries of the transversal Killing horizon coincide with the one defined on the event horizon of the extremal Kerr-Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection
Construction of codimension 1 immersions of spacetime: the exceptional case
International Nuclear Information System (INIS)
Edelen, Dominic G B
2005-01-01
The Frobenius theorem was used in Edelen (2003 Class. Quantum Grav. 20 3661) to obtain a general body of results for the immersion of spacetime in flat spaces of higher dimension. This addendum completes those results for the exceptional case of immersions of codimension 1 where the Frobenius theorem need not be applied. Local actions of the Poincare groups SO(2, 3)--T(5) or SO(1, 4) -- T(5) are used to obtain immersions of spacetime of codimension 1 that involve six arbitrary functions of the four immersion parameters and an arbitrary constant. Explicit calculations are given for several cases. (addendum)
Energy Technology Data Exchange (ETDEWEB)
Furuuchi, Kazuyuki [Manipal Centre for Natural Sciences, Manipal University,Manipal, Karnataka 576104 (India); Koyama, Yoji [National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu 30013, Taiwan R.O.C. (China)
2016-06-21
We continue our investigation of large field inflation models obtained from higher-dimensional gauge theories, initiated in our previous study http://dx.doi.org/10.1088/1475-7516/2015/02/031. We focus on Dante’s Inferno model which was the most preferred model in our previous analysis. We point out the relevance of the IR obstruction to UV completion, which constrains the form of the potential of the massive vector field, under the current observational upper bound on the tensor to scalar ratio. We also show that in simple examples of the potential arising from DBI action of a D5-brane and that of an NS5-brane that the inflation takes place in the field range which is within the convergence radius of the Taylor expansion. This is in contrast to the well known examples of axion monodromy inflation where inflaton takes place outside the convergence radius of the Taylor expansion. This difference arises from the very essence of Dante’s Inferno model that the effective inflaton potential is stretched in the inflaton field direction compared with the potential for the original field.
International Nuclear Information System (INIS)
Furuuchi, Kazuyuki; Koyama, Yoji
2016-01-01
We continue our investigation of large field inflation models obtained from higher-dimensional gauge theories, initiated in our previous study http://dx.doi.org/10.1088/1475-7516/2015/02/031. We focus on Dante’s Inferno model which was the most preferred model in our previous analysis. We point out the relevance of the IR obstruction to UV completion, which constrains the form of the potential of the massive vector field, under the current observational upper bound on the tensor to scalar ratio. We also show that in simple examples of the potential arising from DBI action of a D5-brane and that of an NS5-brane that the inflation takes place in the field range which is within the convergence radius of the Taylor expansion. This is in contrast to the well known examples of axion monodromy inflation where inflaton takes place outside the convergence radius of the Taylor expansion. This difference arises from the very essence of Dante’s Inferno model that the effective inflaton potential is stretched in the inflaton field direction compared with the potential for the original field.
Spherically symmetric static spacetimes in vacuum f(T) gravity
International Nuclear Information System (INIS)
Ferraro, Rafael; Fiorini, Franco
2011-01-01
We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a Banados, Teitelboim and Zanelli-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).
Centrally extended symmetry algebra of asymptotically Goedel spacetimes
International Nuclear Information System (INIS)
Compere, Geoffrey; Detournay, Stephane
2007-01-01
We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras. The subsequent analysis of three-dimensional Goedel black holes indicates that the Virasoro central charge is negative
International Nuclear Information System (INIS)
Raine, D.J.; Heller, M.
1981-01-01
Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics Copernican kinematics Newtonian dynamics the space-time of classical dynamics classical space-time in the presence of gravity the space-time of special relativity the space-time of general relativity solutions and problems in general relativity Mach's principle and the dynamics of space-time theories of inertial mass the integral formation of general relativity and the frontiers of relativity
Approaches to emergent spacetime in gauge/gravity duality
Sully, James Kenneth
2013-08-01
In this thesis we explore approaches to emergent local spacetime in gauge/gravity duality. We first conjecture that every CFT with a large-N type limit and a parametrically large gap in the spectrum of single-trace operators has a local bulk dual. We defend this conjecture by counting consistent solutions to the four-point function in simple scalar models and matching to the number of local interaction terms in the bulk. Next, we proceed to explicitly construct local bulk operators using smearing functions. We argue that this construction allows one to probe inside black hole horizons for only short times. We then suggest that the failure to construct bulk operators inside a black hole at late times is indicative of a break-down of local effective field theory at the black hole horizon. We argue that the postulates of black hole complementarity are inconsistent and cannot be realized within gauge/gravity duality. We argue that the most conservative solution is a firewall at the black hole horizon and we critically explore alternative resolutions. We then examine the CGHS model of two-dimensional gravity to look for dynamical formation of firewalls. We find that the CGHS model does not exhibit firewalls, but rather contains long-lived remnants. We argue that, while this is consistent for the CGHS model, it cannot be so in higher-dimensional theories of gravity. Lastly, we turn to F-theory, and detail local and global obstructions to writing elliptic fibrations in Tate form. We determine more general possible forms.
Regularization and renormalization of quantum field theory in curved space-time
International Nuclear Information System (INIS)
Bernard, C.; Duncan, A.
1977-01-01
It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli-Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by starting always from a manifestly generally covariant action, and the technical limitations of the dimensional reqularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions--it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli-Villars regulated. One then studies a specific solvable two-dimensional model of a massive scalar field in a Robertson-Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well defined finite expectation value for the stress-energy tensor. The particle production (less than 0 in/vertical bar/theta/sup mu nu/(x,t)/vertical bar/0 in greater than for t → + infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t→ +- infinity independently of any weak field approximation. The extension of the model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed
Energy Technology Data Exchange (ETDEWEB)
Silva O, G.; Garcia G, P. [Facultad de Ciencias Fisico Matematicas de la Universidad Autonoma de Puebla, A.P. 1152, 72001 Puebla (Mexico)
2004-07-01
In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three dimensional Minkowski metric. (Author)
Emergent/quantum gravity: macro/micro structures of spacetime
International Nuclear Information System (INIS)
Hu, B L
2009-01-01
Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view general relativity is an effective theory valid only at long wavelengths and low energies. We describe the tasks of emergent gravity from any ('top-down') candidate theory for the microscopic structure of spacetime (quantum gravity), namely, identifying the conditions and processes or mechanisms whereby the familiar macroscopic spacetime described by general relativity and matter content described by quantum field theory both emerge with high probability and reasonable robustness. We point out that this task may not be so easy as commonly conjured (as implied in the 'theory of everything') because there are emergent phenomena which cannot simply be deduced from a given micro-theory. Going in the opposite direction ('bottom-up') is the task of quantum gravity, i.e., finding a theory for the microscopic structure of spacetime, which, in this new view, cannot come from quantizing the metric or connection forms because they are the collective variables which are meaningful only for the macroscopic theory (valid below the Planck energy). This task looks very difficult or almost impossible because it entails reconstructing lost information. We point out that the situation may not be so hopeless if we ask the right questions and have the proper tools for what we want to look for. We suggest pathways to move 'up' (in energy) from the given macroscopic conditions of classical gravity and quantum field theory to the domain closer to the micro-macro interface where spacetime emerged and places to look for clues or tell-tale signs at low energy where one could infer indirectly some salient features of the micro-structure of spacetime.
Dark energy from discrete spacetime.
Directory of Open Access Journals (Sweden)
Aaron D Trout
Full Text Available Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
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
Manifold-splitting regularization, self-linking, twisting, writhing numbers of space-time ribbons
International Nuclear Information System (INIS)
Tze, C.H.
1988-01-01
The authors present an alternative formulation of Polyakov's regularization of Gauss' integral formula for a single closed Feynman path. A key element in his proof of the D = 3 fermi-bose transmutations induced by topological gauge fields, this regularization is linked here with the existence and properties of a nontrivial topological invariant for a closed space ribbon. This self-linking coefficient, an integer, is the sum of two differential characteristics of the ribbon, its twisting and writhing numbers. These invariants form the basis for a physical interpretation of our regularization. Their connection to Polyakov's spinorization is discussed. The authors further generalize their construction to the self-linking, twisting and writhing of higher dimensional d = eta(odd) submanifolds in D = (2eta + 1) space-time
Ringing in de Sitter spacetime
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Alex Buchel
2018-03-01
Full Text Available Hydrodynamics is a universal effective theory describing relaxation of quantum field theories towards equilibrium. Massive QFTs in de Sitter spacetime are never at equilibrium. We use holographic gauge theory/gravity correspondence to describe relaxation of a QFT to its Bunch–Davies vacuum — an attractor of its late-time dynamics. Specifically, we compute the analogue of the quasinormal modes describing the relaxation of a holographic toy model QFT in de Sitter.
Spacetimes containing slowly evolving horizons
International Nuclear Information System (INIS)
Kavanagh, William; Booth, Ivan
2006-01-01
Slowly evolving horizons are trapping horizons that are ''almost'' isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes
Lorentz violations in multifractal spacetimes
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2017-05-15
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E{sub *} > 10{sup 14} GeV (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E{sub *} > 10{sup 17} GeV or greater. (orig.)
Directory of Open Access Journals (Sweden)
Ronald E. Meyers
2015-03-01
Full Text Available We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.
Causal structure of analogue spacetimes
International Nuclear Information System (INIS)
Barcelo, Carlos; Liberati, Stefano; Sonego, Sebastiano; Visser, Matt
2004-01-01
The so-called 'analogue models of general relativity' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved spacetime. Specifically, the propagation of perturbations in these condensed matter systems is described by 'effective metrics' that carry with them notions of 'causal structure' as determined by an exchange of quasi-particles. These quasi-particle-induced causal structures serve as specific examples of what can be done in the presence of a Lorentzian metric without having recourse to the Einstein equations of general relativity. (After all, the underlying analogue model is governed by its own specific physics, not necessarily by the Einstein equations.) In this paper we take a careful look at what can be said about the causal structure of analogue spacetimes, focusing on those containing quasi-particle horizons, both with a view to seeing what is different from standard general relativity, and what the similarities might be. For definiteness, and because the physics is particularly simple to understand, we will phrase much of the discussion in terms of acoustic disturbances in moving fluids, where the underlying physics is ordinary fluid mechanics, governed by the equations of traditional hydrodynamics, and the relevant quasi-particles are the phonons. It must however be emphasized that this choice of example is only for the sake of pedagogical simplicity and that our considerations apply generically to wide classes of analogue spacetimes
Spinors, superalgebras and the signature of space-time
Ferrara, S.
2001-01-01
Superconformal algebras embedding space-time in any dimension and signature are considered. Different real forms of the $R$-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than one times). Application of these superalgebras are found in the context of supergravities with 32 supersymmetries, in any dimension $D \\leq 11$. These theories are related to $D = 11, M, M^*$ and $M^\\prime$ theories or $D = 10$, IIB, IIB$^*$ theories when compactified on Lorentzian tori. All dimensionally reduced theories fall in three distinct phases specified by the number of (128 bosonic) positive and negative norm states: $(n^+,n^-) = (128,0), (64,64), (72,56)$.
Little Randall-Sundrum model and a multiply warped spacetime
International Nuclear Information System (INIS)
McDonald, Kristian L.
2008-01-01
A recent work has investigated the possibility that the mass scale for the ultraviolet (UV) brane in the Randall-Sundrum (RS) model is of the order 10 3 TeV. In this so called 'little Randall-Sundrum' (LRS) model the bounds on the gauge sector are less severe, permitting a lower Kaluza-Klein scale and cleaner discovery channels. However employing a low UV scale nullifies one major appeal of the RS model, namely, the elegant explanation of the hierarchy between the Planck and weak scales. In this work we show that by localizing the gauge, fermion, and scalar sector of the LRS model on a five dimensional slice of a doubly warped spacetime one may obtain the low UV brane scale employed in the LRS model and motivate the weak-Planck hierarchy. We also consider the generalization to an n-warped spacetime
Relativity and the nature of spacetime. 2. ed.
International Nuclear Information System (INIS)
Petkov, Vesselin
2009-01-01
The most important question that is addressed in this book is ''what is the nature (the ontological status) of spacetime?'' or, equivalently, ''what is the dimensionality of the world at the macroscopic level?'' The answer to this question is developed via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional. This analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible. The implications of this result for physics, philosophy, and our entire world view are discussed. This new edition has been significantly expanded with new sections, appendices, notes and references. The arguments of the previous edition are strengthened; new developments in the field are presented and integrated to yield a thoroughly convincing and clear treatment. (orig.)
Gravitational Lensing from a Spacetime Perspective
Directory of Open Access Journals (Sweden)
Perlick Volker
2004-09-01
Full Text Available The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.
Statistics from dynamics in curved spacetime
International Nuclear Information System (INIS)
Parker, L.; Wang, Y.
1989-01-01
We consider quantum fields of spin 0, 1/2, 1, 3/2, and 2 with a nonzero mass in curved spacetime. We show that the dynamical Bogolubov transformations associated with gravitationally induced particle creation imply the connection between spin and statistics: By embedding two flat regions in a curved spacetime, we find that only when one imposes Bose-Einstein statistics for an integer-spin field and Fermi-Dirac statistics for a half-integer-spin field in the first flat region is the same type of statistics propagated from the first to the second flat region. This derivation of the flat-spacetime spin-statistics theorem makes use of curved-spacetime dynamics and does not reduce to any proof given in flat spacetime. We also show in the same manner that parastatistics, up to the fourth order, are consistent with the dynamical evolution of curved spacetime
A comparative study of Dirac quasinormal modes of charged black holes in higher dimensions
International Nuclear Information System (INIS)
Chakrabarti, Sayan K.
2009-01-01
In this work we study the Dirac quasinormal modes of higher dimensional charged black holes. Higher dimensional Reissner-Nordstroem type black holes as well as charged black holes in Einstein-Gauss-Bonnet theories are studied for fermionic perturbations using WKB method. A comparative study of the quasinormal modes in the two different theories of gravity has been performed. The behavior of the frequencies with the variation of black hole parameters as well as with the variation of space-time dimensions is studied. We also study the large multipole number limit of the black hole potential in order to look for an analytic expression for the frequencies. (orig.)
Possibility of extending space-time coordinates
International Nuclear Information System (INIS)
Wang Yongcheng.
1993-11-01
It has been shown that one coordinate system can describe a whole space-time region except some supersurfaces on which there are coordinate singularities. The conditions of extending a coordinate from real field to complex field are studied. It has been shown that many-valued coordinate transformations may help us to extend space-time regions and many-valued metric functions may make one coordinate region to describe more than one space-time regions. (author). 11 refs
Fermion systems in discrete space-time
International Nuclear Information System (INIS)
Finster, Felix
2007-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure
Fermion systems in discrete space-time
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)
2007-05-15
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion Systems in Discrete Space-Time
Finster, Felix
2006-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion systems in discrete space-time
Finster, Felix
2007-05-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Properties of the eleven dimensional supermembrane theory
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Townsend, P.K.
1987-09-01
We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N=8 world volume (rigid) supersymmetry in a ''physical'' gauge; we also present the field equations and transformation rules in a ''lightcone'' gauge. We semiclassically quantize the closed toroidal supermembrane on a spacetime (Minkowski) 4 x (flat 7-torus), and review some mathematical results that are relevant for path integral quantization. (author). 52 refs, 1 fig
Energy Technology Data Exchange (ETDEWEB)
Franck, John M.; Chandrasekaran, Siddarth; Dzikovski, Boris; Dunnam, Curt R.; Freed, Jack H., E-mail: jhf3@cornell.edu [Department of Chemistry and Chemical Biology and National Biomedical Center for Advanced ESR Technology, Cornell University, Ithaca, New York 14853 (United States)
2015-06-07
The development, applications, and current challenges of the pulsed ESR technique of two-dimensional Electron-Electron Double Resonance (2D ELDOR) are described. This is a three-pulse technique akin to 2D Exchange Nuclear Magnetic Resonance, but involving electron spins, usually in the form of spin-probes or spin-labels. As a result, it required the extension to much higher frequencies, i.e., microwaves, and much faster time scales, with π/2 pulses in the 2-3 ns range. It has proven very useful for studying molecular dynamics in complex fluids, and spectral results can be explained by fitting theoretical models (also described) that provide a detailed analysis of the molecular dynamics and structure. We discuss concepts that also appear in other forms of 2D spectroscopy but emphasize the unique advantages and difficulties that are intrinsic to ESR. Advantages include the ability to tune the resonance frequency, in order to probe different motional ranges, while challenges include the high ratio of the detection dead time vs. the relaxation times. We review several important 2D ELDOR studies of molecular dynamics. (1) The results from a spin probe dissolved in a liquid crystal are followed throughout the isotropic → nematic → liquid-like smectic → solid-like smectic → crystalline phases as the temperature is reduced and are interpreted in terms of the slowly relaxing local structure model. Here, the labeled molecule is undergoing overall motion in the macroscopically aligned sample, as well as responding to local site fluctuations. (2) Several examples involving model phospholipid membranes are provided, including the dynamic structural characterization of the boundary lipid that coats a transmembrane peptide dimer. Additionally, subtle differences can be elicited for the phospholipid membrane phases: liquid disordered, liquid ordered, and gel, and the subtle effects upon the membrane, of antigen cross-linking of receptors on the surface of plasma membrane
International Nuclear Information System (INIS)
Franck, John M.; Chandrasekaran, Siddarth; Dzikovski, Boris; Dunnam, Curt R.; Freed, Jack H.
2015-01-01
The development, applications, and current challenges of the pulsed ESR technique of two-dimensional Electron-Electron Double Resonance (2D ELDOR) are described. This is a three-pulse technique akin to 2D Exchange Nuclear Magnetic Resonance, but involving electron spins, usually in the form of spin-probes or spin-labels. As a result, it required the extension to much higher frequencies, i.e., microwaves, and much faster time scales, with π/2 pulses in the 2-3 ns range. It has proven very useful for studying molecular dynamics in complex fluids, and spectral results can be explained by fitting theoretical models (also described) that provide a detailed analysis of the molecular dynamics and structure. We discuss concepts that also appear in other forms of 2D spectroscopy but emphasize the unique advantages and difficulties that are intrinsic to ESR. Advantages include the ability to tune the resonance frequency, in order to probe different motional ranges, while challenges include the high ratio of the detection dead time vs. the relaxation times. We review several important 2D ELDOR studies of molecular dynamics. (1) The results from a spin probe dissolved in a liquid crystal are followed throughout the isotropic → nematic → liquid-like smectic → solid-like smectic → crystalline phases as the temperature is reduced and are interpreted in terms of the slowly relaxing local structure model. Here, the labeled molecule is undergoing overall motion in the macroscopically aligned sample, as well as responding to local site fluctuations. (2) Several examples involving model phospholipid membranes are provided, including the dynamic structural characterization of the boundary lipid that coats a transmembrane peptide dimer. Additionally, subtle differences can be elicited for the phospholipid membrane phases: liquid disordered, liquid ordered, and gel, and the subtle effects upon the membrane, of antigen cross-linking of receptors on the surface of plasma membrane
Simulations of black holes in compactified spacetimes
Energy Technology Data Exchange (ETDEWEB)
Zilhao, Miguel; Herdeiro, Carlos [Centro de Fisica do Porto, Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto (Portugal); Cardoso, Vitor; Nerozzi, Andrea; Sperhake, Ulrich; Witek, Helvi [Centro Multidisciplinar de Astrofisica, Deptartamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Gualtieri, Leonardo, E-mail: mzilhao@fc.up.pt [Dipartimento di Fisica, Universita di Roma ' Sapienza' and Sezione INFN Roma1, P.A. Moro 5, 00185, Roma (Italy)
2011-09-22
From the gauge/gravity duality to braneworld scenarios, black holes in compactified spacetimes play an important role in fundamental physics. Our current understanding of black hole solutions and their dynamics in such spacetimes is rather poor because analytical tools are capable of handling a limited class of idealized scenarios, only. Breakthroughs in numerical relativity in recent years, however, have opened up the study of such spacetimes to a computational treatment which facilitates accurate studies of a wider class of configurations. We here report on recent efforts of our group to perform numerical simulations of black holes in cylindrical spacetimes.
The free Maxwell field in curved spacetime
International Nuclear Information System (INIS)
Kueskue, M.
2001-09-01
The aim of this thesis is to discuss quantizations of the free Maxwell field in flat and curved spacetimes. First we introduce briefly some notions from tensor analysis and the causal structure of spacetime. As an introduction to the main topic, we review some aspects of the two axiomatic quantum field theories, Wightman theory and algebraic quantum field theory. We also give an introduction into concepts of the quantization of fields on curved spacetime backgrounds. Then the wave equation and quantization of the Maxwell field in flat spacetimes is discussed. It follows a review of J. Dimock's quantization of the Maxwell field on curved spacetimes and then we come to our main result: We show explicitly that the Maxwell field, defined by dF=0 and δF=0, has a well posed initial value formulation on arbitrary globally hyperbolic spacetime manifolds. We prove the existence and uniqueness of fundamental solutions without employing a vector potential. Thus our solution is also applicable to spacetimes not satisfying the Poincare lemma and should lead to a quantization of the Maxwell field on non-trivial spacetime backgrounds. This in turn provides the opportunity to investigate physical states on non-trivial spacetime-topologies and could lead to the discovery of new quantum phenomena. (orig.)
Conformal symmetry inheritance in null fluid spacetimes
International Nuclear Information System (INIS)
Tupper, B O J; Keane, A J; Hall, G S; Coley, A A; Carot, J
2003-01-01
We define inheriting conformal Killing vectors for null fluid spacetimes and find the maximum dimension of the associated inheriting Lie algebra. We show that for non-conformally flat null fluid spacetimes, the maximum dimension of the inheriting algebra is seven and for conformally flat null fluid spacetimes the maximum dimension is eight. In addition, it is shown that there are two distinct classes of non-conformally flat generalized plane wave spacetimes which possess the maximum dimension, and one class in the conformally flat case
Wu, Ning
2012-01-01
When we discuss problems on gravity, we can not avoid some fundamental physical problems, such as space-time, inertia, and inertial reference frame. The goal of this paper is to discuss the logic system of gravity theory and the problems of space-time, inertia, and inertial reference frame. The goal of this paper is to set up the theory on space-time in gauge theory of gravity. Based on this theory, it is possible for human kind to manipulate physical space-time on earth, and produce a machin...
Particle creation in inhomogeneous spacetimes
International Nuclear Information System (INIS)
Frieman, J.A.
1989-01-01
We study the creation of particles by inhomogeneous perturbations of spatially flat Friedmann-Robertson-Walker cosmologies. For massless scalar fields, the pair-creation probability can be expressed in terms of geometric quantities (curvature invariants). The results suggest that inhomogeneities on scales up to the particle horizon will be damped out near the Planck time. Perturbations on scales larger than the horizon are explicitly shown to yield no created pairs. The results generalize to inhomogeneous spacetimes several earlier studies of pair creation in homogeneous anisotropic cosmologies
Relativistic helicity and link in Minkowski space-time
International Nuclear Information System (INIS)
Yoshida, Z.; Kawazura, Y.; Yokoyama, T.
2014-01-01
A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves
Classification of non-Riemannian doubled-yet-gauged spacetime
Energy Technology Data Exchange (ETDEWEB)
Morand, Kevin [Universidad Andres Bello, Departamento de Ciencias Fisicas, Santiago de Chile (Chile); Universidad Tecnica Federico Santa Maria, Centro Cientifico-Tecnologico de Valparaiso, Departamento de Fisica, Valparaiso (Chile); Park, Jeong-Hyuck [Sogang University, Department of Physics, Seoul (Korea, Republic of); Institute for Basic Science (IBS), Center for Theoretical Physics of the Universe, Seoul (Korea, Republic of)
2017-10-15
Assuming O(D,D) covariant fields as the 'fundamental' variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n, anti n), 0 ≤ n + anti n ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and anti n directions, respectively, while particles and strings are frozen over the n + anti n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four. (orig.)
Ray trajectories for Alcubierre spacetime
International Nuclear Information System (INIS)
Anderson, Tom H; Mackay, Tom G; Lakhtakia, Akhlesh
2011-01-01
The Alcubierre spacetime was simulated by means of a Tamm medium which is asymptotically identical to vacuum and has constitutive parameters which are continuous functions of the spatial coordinates. Accordingly, the Tamm medium is amenable to physical realization as a micro- or nanostructured metamaterial. A comprehensive characterization of ray trajectories in the Tamm medium was undertaken, within the geometric-optics regime. Propagation directions corresponding to evanescent waves were identified: these occur in the region of the Tamm medium which corresponds to the warp bubble of the Alcubierre spacetime, especially for directions perpendicular to the velocity of the warp bubble at high speeds of that bubble. Ray trajectories are acutely sensitive to the magnitude and direction of the warp bubble's velocity, but rather less sensitive to the thickness of the transition zone between the warp bubble and its background. In particular, for rays which travel in the same direction as the warp bubble, the latter acts as a focusing lens, most notably at high speeds
Dark Energy and Spacetime Symmetry
Directory of Open Access Journals (Sweden)
Irina Dymnikova
2017-03-01
Full Text Available The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum fluid essentially anisotropic and allows it to be evolving and clustering. The relevant solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy: regular black holes, their remnants and self-gravitating vacuum solitons with de Sitter vacuum interiors—which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context spacetime symmetry provides a mechanism for relaxing cosmological constant to a needed non-zero value.
Field, F.; Goodbun, J.; Watson, V.
Architects have a role to play in interplanetary space that has barely yet been explored. The architectural community is largely unaware of this new territory, for which there is still no agreed method of practice. There is moreover a general confusion, in scientific and related fields, over what architects might actually do there today. Current extra-planetary designs generally fail to explore the dynamic and relational nature of space-time, and often reduce human habitation to a purely functional problem. This is compounded by a crisis over the representation (drawing) of space-time. The present work returns to first principles of architecture in order to realign them with current socio-economic and technological trends surrounding the space industry. What emerges is simultaneously the basis for an ecological space architecture, and the representational strategies necessary to draw it. We explore this approach through a work of design-based research that describes the construction of Ocean; a huge body of water formed by the collision of two asteroids at the Translunar Lagrange Point (L2), that would serve as a site for colonisation, and as a resource to fuel future missions. Ocean is an experimental model for extra-planetary space design and its representation, within the autonomous discipline of architecture.
Braverman, Amy; Nguyen, Hai; Olsen, Edward; Cressie, Noel
2011-01-01
Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.
Cosmic Censorship for Gowdy Spacetimes.
Ringström, Hans
2010-01-01
Due to the complexity of Einstein's equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.
Construction of two-dimensional quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Klimek, S.; Kondracki, W.
1987-12-01
We present a sketch of the construction of the functional measure for the SU(2) quantum chromodynamics with one generation of fermions in two-dimensional space-time. The method is based on a detailed analysis of Wilson loops.
Matter fields in curved space-time
International Nuclear Information System (INIS)
Viet, Nguyen Ai; Wali, Kameshwar C.
2000-01-01
We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two sheeted-space time and construct the action functionals that describe their interactions
On Mass, Spacetime Curvature, and Gravity
Janis, Allen I.
2018-01-01
The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students' previous knowledge of spacetime diagrams in special relativity is suggested.
Space-time and matter in 'prephysics'
International Nuclear Information System (INIS)
Terazawa, Hidezumi.
1985-05-01
Many fundamental questions concerning the space-time and matter are asked and answered in ''prephysics'', a new line of physics (or philosophy but not metaphysics). They include the following: 1) ''Why is our space-time of 4 dimensions.'', 2) ''What is the ultimate form of matter.'' and 3) ''How was our universe created.''. (author)
New instabilities of de Sitter spacetimes
International Nuclear Information System (INIS)
Copsey, Keith; Mann, Robert
2010-01-01
We construct an instanton describing the pair production of non-Kaluza-Klein bubbles of nothing in higher odd-dimensional de Sitter spaces. In addition to showing that higher-dimensional de Sitter spaces have a nonzero probability to become topologically nontrivial, this process provides direct evidence for the association of entropy with cosmological horizons as well as evidence that non-Kaluza-Klein bubbles of nothing are a necessary ingredient in string theory or any other consistent quantum theory of gravity in higher dimensions.
ADM Mass for Asymptotically de Sitter Space-Time
International Nuclear Information System (INIS)
Huang Shiming; Yue Ruihong; Jia Dongyan
2010-01-01
In this paper, an ADM mass formula for asymptotically de Sitter(dS) space-time is derived from the energy-momentum tensor. We take the vacuum dS space as the background and investigate the ADM mass of the (d + 3)-dimensional sphere-symmetric space with a positive cosmological constant, and find that the ADM mass of asymptotically dS space is based on the ADM mass of Schwarzschild field and the cosmological background brings some small mass contribution as well. (general)
Dynamics of Robertson–Walker spacetimes with diffusion
Energy Technology Data Exchange (ETDEWEB)
Alho, A., E-mail: aalho@math.ist.utl.pt [Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Lisboa (Portugal); Calogero, S., E-mail: calogero@chalmers.se [Department of Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, Gothenburg (Sweden); Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt [Departamento de Matemática e Aplicações, Universidade do Minho, Guimarães (Portugal); Soares, A.J., E-mail: ajsoares@math.uminho.pt [Centro de Matemática, Universidade do Minho, Braga (Portugal)
2015-03-15
We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.
A heterotic N=2 string with space-time supersymmetry
International Nuclear Information System (INIS)
Bellucci, S.; Galajinsky, A.; Lechtenfeld, O.
2001-02-01
It is reconsidered the issue of embedding space-time fermions into the four dimensional N=2 world-sheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N =4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry
Gravitational charges of transverse asymptotically AdS spacetimes
International Nuclear Information System (INIS)
Cebeci, Hakan; Sarioglu, Oezguer; Tekin, Bayram
2006-01-01
Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such as mass and angular momenta densities) of p-dimensional branes/solitons or any other extended objects that curve the transverse space into an asymptotically flat or AdS one. Our construction answers the question of what kind of charges the antisymmetric Killing-Yano tensors lead to
Spacetime causality in the study of the Hankel tranform
Burnol, J
2006-01-01
We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of the theorem of de~Branges and V.~Rovnyak concerning Hankel pairs with a support property. We recover their isometric expansion as an application of Riemann's general method for solving Cauchy-Goursat problems of hyperbolic type.
Partially massless graviton on beyond Einstein spacetimes
Bernard, Laura; Deffayet, Cédric; Hinterbichler, Kurt; von Strauss, Mikael
2017-06-01
We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes (some, but not all, with vanishing Bach tensors) allowing for the propagation of a partially massless graviton. These include in particular the Einstein static Universe.
Spacetime symmetries and topology in bimetric relativity
Torsello, Francesco; Kocic, Mikica; Högâs, Marcus; Mörtsell, Edvard
2018-04-01
We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.
Constraints on string vacua with spacetime supersymmetry
International Nuclear Information System (INIS)
Banks, T.; California Univ., Santa Cruz; Dixon, L.J.
1988-01-01
We examine the consequences of extended spacetime supersymmetry for classical superstring vacua with four dimensions uncompactified. N=2 spacetime supersymmetry implies that the 'internal' N=1 superconformal algebra with central charge c=6 splits into a piece with c=4 which has N=4 superconformal invariance, and a piece with c=2 which is constructed from two free dimension 1/2 superfields. N=4 spacetime supersymmetry requires that the entire c=6 algebra be represented by six free superfields. Using the world-sheet properties of N=1 spacetime supersymmetric classical vacua, we show that spacetime supersymmetry cannot be continuously broken within a family of classical vacua. Finally, we argue that the effective field theories for classical vacua of superstring theories (whether space time supersymmetric or not) have no continuous global symmetries - all continuous symmetries are gauged. (orig.)
Schwinger functions for the Yukawa model in two dimensions with space-time cutoff
International Nuclear Information System (INIS)
Seiler, E.
1975-01-01
It is shown that a Euclidean version of the formulae of Matthews and Salam for the Green's functions of a two-dimensional Yukawa model with interaction in a finite space-time volume makes sense, if renormalized correctly. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Li, Huai-Fan; Zhao, Hui-Hua; Zhang, Li-Chun; Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China)
2017-05-15
Using Maxwell's equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P-v diagrams. The two-phase equilibrium curves in the P-T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems. (orig.)
Poole, Dana S; Plenge, Esben; Poot, Dirk H J; Lakke, Egbert A J F; Niessen, Wiro J; Meijering, Erik; van der Weerd, Louise
2014-07-01
The visualization of activity in mouse brain using inversion recovery spin echo (IR-SE) manganese-enhanced MRI (MEMRI) provides unique contrast, but suffers from poor resolution in the slice-encoding direction. Super-resolution reconstruction (SRR) is a resolution-enhancing post-processing technique in which multiple low-resolution slice stacks are combined into a single volume of high isotropic resolution using computational methods. In this study, we investigated, first, whether SRR can improve the three-dimensional resolution of IR-SE MEMRI in the slice selection direction, whilst maintaining or improving the contrast-to-noise ratio of the two-dimensional slice stacks. Second, the contrast-to-noise ratio of SRR IR-SE MEMRI was compared with a conventional three-dimensional gradient echo (GE) acquisition. Quantitative experiments were performed on a phantom containing compartments of various manganese concentrations. The results showed that, with comparable scan times, the signal-to-noise ratio of three-dimensional GE acquisition is higher than that of SRR IR-SE MEMRI. However, the contrast-to-noise ratio between different compartments can be superior with SRR IR-SE MEMRI, depending on the chosen inversion time. In vivo experiments were performed in mice receiving manganese using an implanted osmotic pump. The results showed that SRR works well as a resolution-enhancing technique in IR-SE MEMRI experiments. In addition, the SRR image also shows a number of brain structures that are more clearly discernible from the surrounding tissues than in three-dimensional GE acquisition, including a number of nuclei with specific higher brain functions, such as memory, stress, anxiety and reward behavior. Copyright © 2014 John Wiley & Sons, Ltd.
On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
Energy Technology Data Exchange (ETDEWEB)
Nilsson, Bengt E.W. [Fundamental Physics, Chalmers University of Technology,SE-412 96 Göteborg (Sweden)
2016-08-24
We propose field equations for the conformal higher spin system in three dimensions coupled to a conformal scalar field with a sixth order potential. Both the higher spin equation and the unfolded equation for the scalar field have source terms and are based on a conformal higher spin algebra which we treat as an expansion in multi-commutators. Explicit expressions for the source terms are suggested and subjected to some simple tests. We also discuss a cascading relation between the Chern-Simons action for the higher spin gauge theory and an action containing a term for each spin that generalizes the spin 2 Chern-Simons action in terms of the spin connection expressed in terms of the frame field. This cascading property is demonstrated in the free theory for spin 3 but should work also in the complete higher spin theory.
Higher point spin field correlators in D=4 superstring theory
International Nuclear Information System (INIS)
Haertl, D.; Schlotterer, O.; Stieberger, S.
2010-01-01
Calculational tools are provided allowing to determine general tree-level scattering amplitudes for processes involving bosons and fermions in heterotic and superstring theories in four space-time dimensions. We compute higher-point superstring correlators involving massless four-dimensional fermionic and spin fields. In D=4 these correlators boil down to a product of two pure spin field correlators of left- and right-handed spin fields. This observation greatly simplifies the computation of such correlators. The latter are basic ingredients to compute multi-fermion superstring amplitudes in D=4. Their underlying fermionic structure and the fermionic couplings in the effective action are determined by these correlators.
Newtonian gravity on quantum spacetime
Directory of Open Access Journals (Sweden)
Majid Shahn
2014-04-01
Full Text Available The bicrossproduct model λ-Minkowski (or ‘κ-Minkowski’ quantum space-time has an anomaly for the action of the Poincaré quantum group which was resolved by an extra cotangent direction θ’ not visible classically. We show that gauging a coefficient of θ′ introduces gravity into the model. We solve and analyse the model nonrelativisticaly in a 1/r potential, finding an induced constant term in the effective potential energy and a weakening and separation of the effective gravitational and inertial masses as the test particle Klein-Gordon mass increases. The present work is intended as a proof of concept but the approach could be relevant to an understanding of dark energy and possibly to macroscopic quantum systems.
Bubble Collision in Curved Spacetime
International Nuclear Information System (INIS)
Hwang, Dong-il; Lee, Bum-Hoon; Lee, Wonwoo; Yeom, Dong-han
2014-01-01
We study vacuum bubble collisions in curved spacetime, in which vacuum bubbles were nucleated in the initial metastable vacuum state by quantum tunneling. The bubbles materialize randomly at different times and then start to grow. It is known that the percolation by true vacuum bubbles is not possible due to the exponential expansion of the space among the bubbles. In this paper, we consider two bubbles of the same size with a preferred axis and assume that two bubbles form very near each other to collide. The two bubbles have the same field value. When the bubbles collide, the collided region oscillates back-and-forth and then the collided region eventually decays and disappears. We discuss radiation and gravitational wave resulting from the collision of two bubbles
Toward a holographic theory for general spacetimes
Nomura, Yasunori; Salzetta, Nico; Sanches, Fabio; Weinberg, Sean J.
2017-04-01
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct-sum and "spacetime-equals-entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.
Quantum universe on extremely small space-time scales
International Nuclear Information System (INIS)
Kuzmichev, V.E.; Kuzmichev, V.V.
2010-01-01
The semiclassical approach to the quantum geometrodynamical model is used for the description of the properties of the Universe on extremely small space-time scales. Under this approach, the matter in the Universe has two components of the quantum nature which behave as antigravitating fluids. The first component does not vanish in the limit h → 0 and can be associated with dark energy. The second component is described by an extremely rigid equation of state and goes to zero after the transition to large spacetime scales. On small space-time scales, this quantum correction turns out to be significant. It determines the geometry of the Universe near the initial cosmological singularity point. This geometry is conformal to a unit four-sphere embedded in a five-dimensional Euclidean flat space. During the consequent expansion of the Universe, when reaching the post-Planck era, the geometry of the Universe changes into that conformal to a unit four-hyperboloid in a five-dimensional Lorentzsignatured flat space. This agrees with the hypothesis about the possible change of geometry after the origin of the expanding Universe from the region near the initial singularity point. The origin of the Universe can be interpreted as a quantum transition of the system from a region in the phase space forbidden for the classical motion, but where a trajectory in imaginary time exists, into a region, where the equations of motion have the solution which describes the evolution of the Universe in real time. Near the boundary between two regions, from the side of real time, the Universe undergoes almost an exponential expansion which passes smoothly into the expansion under the action of radiation dominating over matter which is described by the standard cosmological model.
QCD-instantons and conformal space-time inversion symmetry
International Nuclear Information System (INIS)
Klammer, D.
2008-04-01
In this paper, we explore the appealing possibility that the strong suppression of large-size QCD instantons - as evident from lattice data - is due to a surviving conformal space-time inversion symmetry. This symmetry is both suggested from the striking invariance of highquality lattice data for the instanton size distribution under inversion of the instanton size ρ→(left angle ρ right angle 2 )/(ρ) and from the known validity of space-time inversion symmetry in the classical instanton sector. We project the instanton calculus onto the four-dimensional surface of a five-dimensional sphere via conformal stereographic mapping, before investigating conformal inversion. This projection to a compact, curved geometry is both to avoid the occurence of divergences and to introduce the average instanton size left angle ρ right angle from the lattice data as a new length scale. The average instanton size is identified with the radius b of this 5d-sphere and acts as the conformal inversion radius. For b= left angle ρ right angle, our corresponding results are almost perfectly symmetric under space-time inversion and in good qualitative agreement with the lattice data. For (ρ)/(b)→0 we recover the familiar results of instanton perturbation theory in flat 4d-space. Moreover, we illustrate that a (weakly broken) conformal inversion symmetry would have significant consequences for QCD beyond instantons. As a further successful test for inversion symmetry, we present striking implications for another instanton dominated lattice observable, the chirality-flip ratio in the QCD vacuum. (orig.)
Unification of gauge and gravity Chern-Simons theories in 3-D space-time
Energy Technology Data Exchange (ETDEWEB)
Saghir, Chireen A.; Shamseddine, Laurence W. [American University of Beirut, Physics Department, Beirut (Lebanon)
2017-11-15
Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge group we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3-D space-time. Such a unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3-dimensional space-time manifold on which they are defined. (orig.)
Topology and Singularities in Cosmological Spacetimes Obeying the Null Energy Condition
Galloway, Gregory J.; Ling, Eric
2018-06-01
We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3 + 1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.
DEFF Research Database (Denmark)
Tastu, Julija; Pinson, Pierre; Madsen, Henrik
2015-01-01
-correlations. Estimation is performed in a maximum likelihood framework. Based on a test case application in Denmark, with spatial dependencies over 15 areas and temporal ones for 43 hourly lead times (hence, for a dimension of n = 645), it is shown that accounting for space-time effects is crucial for generating skilful......Emphasis is placed on generating space-time trajectories of wind power generation, consisting of paths sampled from high-dimensional joint predictive densities, describing wind power generation at a number of contiguous locations and successive lead times. A modelling approach taking advantage...
Spacetime averaging of exotic singularity universes
International Nuclear Information System (INIS)
Dabrowski, Mariusz P.
2011-01-01
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
Semiclassical expanding discrete space-times
International Nuclear Information System (INIS)
Cobb, W.K.; Smalley, L.L.
1981-01-01
Given the close ties between general relativity and geometry one might reasonably expect that quantum effects associated with gravitation might also be tied to the geometry of space-time, namely, to some sort of discreteness in space-time itself. In particular it is supposed that space-time consists of a discrete lattice of points rather than the usual continuum. Since astronomical evidence seems to suggest that the universe is expanding, the lattice must also expand. Some of the implications of such a model are that the proton should presently be stable, and the universe should be closed although the mechanism for closure is quantum mechanical. (author)
Physics in space-time with scale-dependent metrics
Balankin, Alexander S.
2013-10-01
We construct three-dimensional space Rγ3 with the scale-dependent metric and the corresponding Minkowski space-time Mγ,β4 with the scale-dependent fractal (DH) and spectral (DS) dimensions. The local derivatives based on scale-dependent metrics are defined and differential vector calculus in Rγ3 is developed. We state that Mγ,β4 provides a unified phenomenological framework for dimensional flow observed in quite different models of quantum gravity. Nevertheless, the main attention is focused on the special case of flat space-time M1/3,14 with the scale-dependent Cantor-dust-like distribution of admissible states, such that DH increases from DH=2 on the scale ≪ℓ0 to DH=4 in the infrared limit ≫ℓ0, where ℓ0 is the characteristic length (e.g. the Planck length, or characteristic size of multi-fractal features in heterogeneous medium), whereas DS≡4 in all scales. Possible applications of approach based on the scale-dependent metric to systems of different nature are briefly discussed.
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.)
The dimensional reduction in a multi-dimensional cosmology
International Nuclear Information System (INIS)
Demianski, M.; Golda, Z.A.; Heller, M.; Szydlowski, M.
1986-01-01
Einstein's field equations are solved for the case of the eleven-dimensional vacuum spacetime which is the product R x Bianchi V x T 7 , where T 7 is a seven-dimensional torus. Among all possible solutions, the authors identify those in which the macroscopic space expands and the microscopic space contracts to a finite size. The solutions with this property are 'typical' within the considered class. They implement the idea of a purely dynamical dimensional reduction. (author)
International Nuclear Information System (INIS)
Akarsu, Özgür; Dereli, Tekin
2013-01-01
We present cosmological solutions for (1+3+n)-dimensional steady state universe in dilaton gravity with an arbitrary dilaton coupling constant w and exponential dilaton self-interaction potentials in the string frame. We focus particularly on the class in which the 3-space expands with a time varying deceleration parameter. We discuss the number of the internal dimensions and the value of the dilaton coupling constant to determine the cases that are consistent with the observed universe and the primordial nucleosynthesis. The 3-space starts with a decelerated expansion rate and evolves into accelerated expansion phase subject to the values of w and n, but ends with a Big Rip in all cases. We discuss the cosmological evolution in further detail for the cases w = 1 and w = ½ that permit exact solutions. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the internal dimensions and thinks that the conventional general relativity is valid at cosmological scales
Akarsu, Özgür; Dereli, Tekin
2013-02-01
We present cosmological solutions for (1+3+n)-dimensional steady state universe in dilaton gravity with an arbitrary dilaton coupling constant w and exponential dilaton self-interaction potentials in the string frame. We focus particularly on the class in which the 3-space expands with a time varying deceleration parameter. We discuss the number of the internal dimensions and the value of the dilaton coupling constant to determine the cases that are consistent with the observed universe and the primordial nucleosynthesis. The 3-space starts with a decelerated expansion rate and evolves into accelerated expansion phase subject to the values of w and n, but ends with a Big Rip in all cases. We discuss the cosmological evolution in further detail for the cases w = 1 and w = ½ that permit exact solutions. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the internal dimensions and thinks that the conventional general relativity is valid at cosmological scales.
Directory of Open Access Journals (Sweden)
Farhad A. Namin
2016-08-01
Full Text Available A rigorous method for obtaining the diffraction patterns of quasicrystals is presented. Diffraction patterns are an essential analytical tool in the study of quasicrystals, since they can be used to determine their photonic resonances. Previous methods for approximating the diffraction patterns of quasicrystals have relied on evaluating the Fourier transform of finite-sized super-lattices. Our approach, on the other hand, is exact in the sense that it is based on a technique that embeds quasicrystals into higher dimensional periodic hyper-lattices, thereby completely capturing the properties of the infinite structure. The periodicity of the unit cell in the higher dimensional space can be exploited to obtain the Fourier series expansion in closed-form of the corresponding atomic surfaces. The utility of the method is demonstrated by applying it to one-dimensional Fibonacci and two-dimensional Penrose quasicrystals. The results are verified by comparing them to those obtained by using the conventional super-lattice method. It is shown that the conventional super-cell approach can lead to inaccurate results due to the continuous nature of the Fourier transform, since quasicrystals have a discrete spectrum, whereas the approach introduced in this paper generates discrete Fourier harmonics. Furthermore, the conventional approach requires very large super-cells and high-resolution sampling of the reciprocal space in order to produce accurate results leading to a very large computational burden, whereas the proposed method generates accurate results with a relatively small number of terms. Finally, we propose how this approach can be generalized from the vertex model, which assumes identical particles at all vertices, to a more realistic case where the quasicrystal is composed of different atoms.
Classical aspects of higher spin topologically massive gravity
International Nuclear Information System (INIS)
Chen Bin; Long Jiang; Zhang Jiandong
2012-01-01
We study the classical solutions of three-dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first-order formulation. The action of higher spin TMG has been proposed by Chen and Long (2011 J. High Energy Phys. JHEP12(2011)114) to be of a Chern–Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS 3 gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair and find that the non-vanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of a special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors. (paper)
Exactly solvable string models of curved space-time backgrounds
Russo, J.G.; Russo, J G; Tseytlin, A A
1995-01-01
We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the dilatonic Melvin solution and the uniform magnetic field solution discussed earlier as well as some singular space-times. Solvability of the string sigma model is related to its connection via duality to a much simpler looking model which is a "twisted" product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model as well as a number of generalizations leading to larger classes of exact 4-dimensional string solutions.
Homotheties of cylindrically symmetric static spacetimes
International Nuclear Information System (INIS)
Qadir, A.; Ziad, M.; Sharif, M.
1998-08-01
In this note we consider the homotheties of cylindrically symmetric static spacetimes. We find that we can provide a complete list of all metrics that admit non-trivial homothetic motions and are cylindrically symmetric static. (author)
Classical field theory in the space of reference frames. [Space-time manifold, action principle
Energy Technology Data Exchange (ETDEWEB)
Toller, M [Dipartimento di Matematica e Fisica, Libera Universita, Trento (Italy)
1978-03-11
The formalism of classical field theory is generalized by replacing the space-time manifold M by the ten-dimensional manifold S of all the local reference frames. The geometry of the manifold S is determined by ten vector fields corresponding to ten operationally defined infinitesimal transformations of the reference frames. The action principle is written in terms of a differential 4-form in the space S (the Lagrangian form). Densities and currents are represented by differential 3-forms in S. The field equations and the connection between symmetries and conservation laws (Noether's theorem) are derived from the action principle. Einstein's theory of gravitation and Maxwell's theory of electromagnetism are reformulated in this language. The general formalism can also be used to formulate theories in which charge, energy and momentum cannot be localized in space-time and even theories in which a space-time manifold cannot be defined exactly in any useful way.
Quantum corrections in thermal states of fermions on anti-de Sitter space-time
Ambruş, Victor E.; Winstanley, Elizabeth
2017-12-01
We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.
Miyamoto, K.; Hoshino, T.; Hitotsubashi, R.; Yamashita, M.; Ueda, J.
In STS-95 space experiments, etiolated pea seedlings grown under microgravity conditions in space have shown to be automorphosis. Epicotyls were almost straight but the most oriented toward the direction far from their cotyledons with ca. 45 degrees from the vertical line as compared with that on earth. In order to know the mechanism of microgravity conditions in space to induce automorphosis, we introduced simulated microgravity conditions on a 3-dimensional clinostat, resulting in the successful induction of automorphosis-like growth and development. Kinetic studies revealed that epicotyls bent at their basal region or near cotyledonary node toward the direction far from the cotyledons with about 45 degrees in both seedlings grown on 1 g and under simulated microgravity conditions on the clinostat within 48 hrs after watering. Thereafter epicotyls grew keeping this orientation under simulated microgravity conditions on the clinostat, whereas those grown on 1 g changed the growth direction to vertical direction by negative gravitropic response. Automorphosis-like growth and development was induced by the application of auxin polar transport inhibitors (2,3,5-triiodobenzoic acid, N-(1-naphtyl)phthalamic acid, 9-hydroxyfluorene-9-carboxylic acid), but not an anti-auxin, p-chlorophenoxyisobutyric acid. Automorphosis-like epicotyl bending was also phenocopied by the application of inhibitors of stretch-activated channel, LaCl3 and GdCl3, and by the application of an inhibitor of protein kinase, cantharidin. These results suggest that automorphosis-like growth in epicotyls of etiolated pea seedlings is due to suppression of negative gravitropic responses on 1 g, and the growth and development of etiolated pea seedlings under 1 g conditions requires for normal activities of auxin polar transport and the gravisensing system relating to calcium channels. Possible mechanisms of perception and transduction of gravity signals to induce automorphosis are discussed.
Minkowski space-time is locally extendible
International Nuclear Information System (INIS)
Beem, J.K.
1980-01-01
An example of a real analytic local extension of Minkowski space-time is given in this note. This local extension is not across points of the b-boundary since Minkowski space-time has an empty b-boundary. Furthermore, this local extension is not across points of the causal boundary. The example indicates that the concept of local inextendibility may be less useful than originally envisioned. (orig.)
Conformal mechanics in Newton-Hooke spacetime
International Nuclear Information System (INIS)
Galajinsky, Anton
2010-01-01
Conformal many-body mechanics in Newton-Hooke spacetime is studied within the framework of the Lagrangian formalism. Global symmetries and Noether charges are given in a form convenient for analyzing the flat space limit. N=2 superconformal extension is built and a new class on N=2 models related to simple Lie algebras is presented. A decoupling similarity transformation on N=2 quantum mechanics in Newton-Hooke spacetime is discussed.
Spacetimes admitting a universal redshift function
International Nuclear Information System (INIS)
Dautcourt, G.
1987-01-01
The conditions are given for a velocity congruence in a Riemannian spacetime admitting a universal redshift function R. This function allows to calculate in a simple way (as a quotient of R values taken at the emission and registration event) the redshift or blueshift connected with an emitter and observer both following the congruence. Spacetimes and congruences with an universal redshift function are shortly discussed. (author)
On discrete models of space-time
International Nuclear Information System (INIS)
Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.
1992-02-01
Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)
Space-Time Disarray and Visual Awareness
Directory of Open Access Journals (Sweden)
Jan Koenderink
2012-04-01
Full Text Available Local space-time scrambling of optical data leads to violent jerks and dislocations. On masking these, visual awareness of the scene becomes cohesive, with dislocations discounted as amodally occluding foreground. Such cohesive space-time of awareness is technically illusory because ground truth is jumbled whereas awareness is coherent. Apparently the visual field is a construction rather than a (veridical perception.
Simulating triangulations. Graphs, manifolds and (quantum) spacetime
International Nuclear Information System (INIS)
Krueger, Benedikt
2016-01-01
Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used
Simulating triangulations. Graphs, manifolds and (quantum) spacetime
Energy Technology Data Exchange (ETDEWEB)
Krueger, Benedikt
2016-07-01
Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used
Quantum fields in curved space-times
International Nuclear Information System (INIS)
Ashtekar, A.; Magnon, A.
1975-01-01
The problem of obtaining a quantum description of the (real) Klein-Gordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is constructed explicitly and the problem of finding its *-representation is reduced to that of selecting a suitable complex structure on the real vector space of the solutions of the (classical) Klein-Gordon equation. Since, in a static space-time, there already exists, a satisfactory quantum field theory, in this case one already knows what the 'correct' complex structure is. A physical characterization of this 'correct' complex structure is obtained. This characterization is used to extend quantum field theory to non-static space-times. Stationary space-times are considered first. In this case, the issue of extension is completely straightforward and the resulting theory is the natural generalization of the one in static space-times. General, non-stationary space-times are then considered. In this case the issue of extension is quite complicated and only a plausible extension is presented. Although the resulting framework is well-defined mathematically, the physical interpretation associated with it is rather unconventional. Merits and weaknesses of this framework are discussed. (author)
Extended system of space-time coordinates and generalized translation group of transformations
International Nuclear Information System (INIS)
Yamaleev, R.M.
1980-01-01
A method of extending space-time is considered. In the nonrelativistic case extending goes by joining a scalar to the 3-dimensional radius-vector, completing this to a quaternion. The interpretation of scalar obtained as a parameter of scale transfornation of the generalized translation of group of transformations is given. Some basic expressions of nonrelativistic classical mechanics in the quaternion representation are given. In the relativistic case space-time is constructed from two quaternions: the first one consists of a pair scalar-3-dimensional radius-vector; the second one, of a pair-time-scalar-3-dimensional time-vector. Time and space coordinates, enter into the expression with the opposite signature. The introduction of a time-vector as well as of a new scalar is stipulated by the requirement of the principle of conforming quantum mechanics of the 1/2 spin to classical mechanics [ru
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
Quantum gravity from noncommutative spacetime
International Nuclear Information System (INIS)
Lee, Jungjai; Yang, Hyunseok
2014-01-01
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Hubble expansion in static spacetime
International Nuclear Information System (INIS)
Rossler, Otto E.; Froehlich, Dieter; Movassagh, Ramis; Moore, Anthony
2007-01-01
A recently proposed mechanism for light-path expansion in a static spacetime is based on the moving-lenses paradigm. Since the latter is valid independently of whether space expands or not, a static universe can be used to better see the implications. The moving-lenses paradigm is related to the paradigm of dynamical friction. If this is correct, a Hubble-like law is implicit. It is described quantitatively. A bent in the Hubble-like line is predictably implied. The main underlying assumption is Price's Principle (PI 3 ). If the theory is sound, the greatest remaining problem in cosmology becomes the origin of hydrogen. Since Blandford's jet production mechanism for quasars is too weak, a generalized Hawking radiation hidden in the walls of cosmic voids is invoked. A second prediction is empirical: slow pattern changes in the cosmic microwave background. A third is ultra-high redshifts for Giacconi quasars. Bruno's eternal universe in the spirit of Augustine becomes a bit less outlandish
Thermodynamics of quantum spacetime histories
Smolin, Lee
2017-11-01
We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez [Phys. Rev. D 87, 121503 (2013); , 10.1103/PhysRevD.87.121503Phys. Rev. D 89, 084069 (2014); , 10.1103/PhysRevD.89.084069Phys. Rev. Lett. 107, 241301 (2011); , 10.1103/PhysRevLett.107.241301Phys. Rev. Lett.108, 169901(E) (2012)., 10.1103/PhysRevLett.108.169901] and Bianchi [arXiv:1204.5122.]. This allows us to apply a recent argument of Jacobson [Phys. Rev. Lett. 116, 201101 (2016).10.1103/PhysRevLett.116.201101] to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.
Quantum gravity from noncommutative spacetime
Energy Technology Data Exchange (ETDEWEB)
Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)
2014-12-15
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Decoherence and disentanglement of qubits detecting scalar fields in an expanded spacetime
Energy Technology Data Exchange (ETDEWEB)
Li, Yujie; Dai, Yue [Fudan University, Department of Physics and State Key Laboratory of Surface Physics, Shanghai (China); Shi, Yu [Fudan University, Department of Physics and State Key Laboratory of Surface Physics, Shanghai (China); Fudan University, Collaborative Innovation Center of Advanced Microstructures, Shanghai (China)
2017-09-15
We consider Unruh-Wald qubit detector model adopted for the far future region of an exactly solvable 1 + 1 dimensional scalar field theory in a toy model of Robertson-Walker expanding spacetime. It is shown that the expansion of the spacetime in its history enhances the decoherence of the qubit coupled with a scalar field. Moreover, we consider two entangled qubits, each locally coupled with a scalar field. The expansion of the spacetime in its history degrades the entanglement between the qubits, and it can lead to entanglement's sudden death if the initial entanglement is small enough. The details depend on the parameters characterizing the expansion of the spacetime. This work, on a toy model, suggests that the history of the spacetime might be probed through the coherent and entanglement behavior of the future detectors of quantum fields. In the present toy model, the two cosmological parameters can be determined from the quantum informational quantities of the detectors. (orig.)
Ono, Toshiaki; Ishihara, Asahi; Asada, Hideki
2017-11-01
By using the Gauss-Bonnet theorem, the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime has been recently discussed, especially by taking account of the finite distance from a lens object to a light source and a receiver [Ishihara, Suzuki, Ono, Asada, Phys. Rev. D 95, 044017 (2017), 10.1103/PhysRevD.95.044017]. We discuss a possible extension of the method of calculating the bending angle of light to stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we consider the light rays on the equatorial plane in the axisymmetric spacetime. We introduce a spatial metric to define the bending angle of light in the finite-distance situation. We show that the proposed bending angle of light is coordinate-invariant by using the Gauss-Bonnet theorem. The nonvanishing geodesic curvature of the photon orbit with the spatial metric is caused in gravitomagnetism, even though the light ray in the four-dimensional spacetime follows the null geodesic. Finally, we consider Kerr spacetime as an example in order to examine how the bending angle of light is computed by the present method. The finite-distance correction to the gravitomagnetic deflection angle due to the Sun's spin is around a pico-arcsecond level. The finite-distance corrections for Sgr A* also are estimated to be very small. Therefore, the gravitomagnetic finite-distance corrections for these objects are unlikely to be observed with present technology.
Is space-time symmetry a suitable generalization of parity-time symmetry?
International Nuclear Information System (INIS)
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-01-01
We discuss space-time symmetric Hamiltonian operators of the form H=H 0 +igH ′ , where H 0 is Hermitian and g real. H 0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G ′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
Study of three-dimensional PET and MR image registration based on higher-order mutual information
International Nuclear Information System (INIS)
Ren Haiping; Chen Shengzu; Wu Wenkai; Yang Hu
2002-01-01
Mutual information has currently been one of the most intensively researched measures. It has been proven to be accurate and effective registration measure. Despite the general promising results, mutual information sometimes might lead to misregistration because of neglecting spatial information and treating intensity variations with undue sensitivity. An extension of mutual information framework was proposed in which higher-order spatial information regarding image structures was incorporated into the registration processing of PET and MR. The second-order estimate of mutual information algorithm was applied to the registration of seven patients. Evaluation from Vanderbilt University and authors' visual inspection showed that sub-voxel accuracy and robust results were achieved in all cases with second-order mutual information as the similarity measure and with Powell's multidimensional direction set method as optimization strategy