Kastor-Traschen black holes, null geodesics and conformal circles

International Nuclear Information System (INIS)

Casey, Stephen

2012-01-01

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

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

Directory of Open Access Journals (Sweden)

Timothy M. Adamo

2009-09-01

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

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

Directory of Open Access Journals (Sweden)

Timothy M. Adamo

2012-01-01

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

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

Science.gov (United States)

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

2012-01-01

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

Maxwell fields and shear-free null geodesic congruences

International Nuclear Information System (INIS)

Newman, Ezra T

2004-01-01

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

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

Science.gov (United States)

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

2018-01-01

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

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

International Nuclear Information System (INIS)

Stuchlik, Z.; Calvani, M.

1990-02-01

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

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

International Nuclear Information System (INIS)

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

1987-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1987-07-01

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

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

International Nuclear Information System (INIS)

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

1987-01-01

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

Do electromagnetic waves always propagate along null geodesics?

International Nuclear Information System (INIS)

Asenjo, Felipe A; Hojman, Sergio A

2017-01-01

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

Asymptotically shear-free and twist-free null geodesic congruences

International Nuclear Information System (INIS)

Kozameh, Carlos; Newman, Ezra T

2007-01-01

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

Twisting null geodesic congruences and the Einstein-Maxwell equations

International Nuclear Information System (INIS)

Newman, Ezra T; Silva-Ortigoza, Gilberto

2006-01-01

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

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

International Nuclear Information System (INIS)

Kupeli, A.H.

1988-01-01

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

Geodesic stability, Lyapunov exponents, and quasinormal modes

International Nuclear Information System (INIS)

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

2009-01-01

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

Optics of relativistic sources in a spherically symmetric gravitational field

International Nuclear Information System (INIS)

Campbell, G.A.

1975-01-01

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

Revisiting scalar geodesic synchrotron radiation in Kerr spacetime

International Nuclear Information System (INIS)

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

2011-01-01

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

Geodesic deviation and Minikowski space

International Nuclear Information System (INIS)

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

1990-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-06-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-07-01

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

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

International Nuclear Information System (INIS)

Yang Xiaolin; Wang Jiancheng

2013-01-01

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

Schwarzschild black hole in the background of the Einstein universe: some physical effects

International Nuclear Information System (INIS)

Ramachandra, B S; Vishveshwara, C V

2002-01-01

A prototype of an asymptotically non-flat black hole spacetime is that of a Schwarzschild black hole in the background of the Einstein universe, which is a special case of the representation of a black hole in a cosmological background given by Vaidya. Recently, this spacetime has been studied in detail by Nayak et al. They constructed a composite spacetime called the Vaidya-Einstein-Schwarzschild (VES) spacetime. We investigate some of the physical effects inherent to this spacetime. We carry out a background-black hole decomposition of the spacetime in order to separate out the effects due to the background spacetime and the black hole. The physical effects we study include the classical tests - the gravitational redshift, perihelion precession and light bending - and circular geodesics. A detailed classification of geodesics, in general, is also given

Interactive visualization of a thin disc around a Schwarzschild black hole

International Nuclear Information System (INIS)

Müller, Thomas; Frauendiener, Jörg

2012-01-01

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

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

International Nuclear Information System (INIS)

Barack, Leor; Sago, Norichika

2011-01-01

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

Null solution of the Yang-Mills equations

International Nuclear Information System (INIS)

Tafel, J.

1986-05-01

We investigate the correspondence between null solutions of the Yang-Mills equations and shearfree geodesic null congruences. We give an example of a non-Abelian null solution with twisting rays. (orig.)

Black hole decay as geodesic motion

International Nuclear Information System (INIS)

Gupta, Kumar S.; Sen, Siddhartha

2003-01-01

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

Quantum correlator outside a Schwarzschild black hole

Directory of Open Access Journals (Sweden)

Claudia Buss

2018-01-01

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

ISCO and Principal Null Congruences in Extremal Kerr Spacetime

International Nuclear Information System (INIS)

Pradhan, Parthapratim

2012-01-01

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

Stability of geodesic imcompleteness for Robertson-Walker space-times

International Nuclear Information System (INIS)

Beem, J.K.

1981-01-01

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

Geodesic in Godel type universes

International Nuclear Information System (INIS)

Galvao, M.O.

1985-01-01

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

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

International Nuclear Information System (INIS)

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

2005-01-01

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

A Statistical Mechanical Problem in Schwarzschild Spacetime

OpenAIRE

Collas, Peter; Klein, David

2006-01-01

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.

On the Penrose inequality along null hypersurfaces

International Nuclear Information System (INIS)

Mars, Marc; Soria, Alberto

2016-01-01

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a functional on surfaces and studying its properties along a null hypersurface Ω extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawking energy along a specific class of geodesic foliations called Geodesic Asymptotically Bondi (GAB), which are shown to always exist. Whenever this foliation approaches large spheres, this inequality becomes the null Penrose inequality and we recover the results of Ludvigsen–Vickers (1983 J. Phys. A: Math. Gen. 16 3349–53) and Bergqvist (1997 Class. Quantum Grav. 14 2577–83). By exploiting further properties of the functional along general geodesic foliations, we introduce an approach to the null Penrose inequality called the Renormalized Area Method and find a set of two conditions which imply the validity of the null Penrose inequality. One of the conditions involves a limit at infinity and the other a restriction on the spacetime curvature along the flow. We investigate their range of applicability in two particular but interesting cases, namely the shear-free and vacuum case, where the null Penrose inequality is known to hold from the results by Sauter (2008 PhD Thesis Zürich ETH ), and the case of null shells propagating in the Minkowski spacetime. Finally, a general inequality bounding the area of the quasi-local black hole in terms of an asymptotic quantity intrinsic of Ω is derived. (paper)

Geodesic flows in a charged black hole spacetime with quintessence

Energy Technology Data Exchange (ETDEWEB)

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

2017-08-15

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

Geodesic flows in a charged black hole spacetime with quintessence

International Nuclear Information System (INIS)

Nandan, Hemwati; Uniyal, Rashmi

2017-01-01

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

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

International Nuclear Information System (INIS)

Fortunato, D.; Masiello, A.

1995-01-01

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

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

Science.gov (United States)

Araya Quezada, Ignacio Jesus

In this thesis, we discuss two different contexts where the idea of gauge symmetry and duality is used to solve the dynamics of physical systems. The first of such contexts is 2T-physics in the worldline in d+2 dimensions, where the principle of Sp(2,R) gauge symmetry in phase space is used to relate different 1T systems in (d -- 1) + 1 dimensions, such as a free relativistic particle, and a relativistic particle in an arbitrary V(x2) potential. Because each 1T shadow system corresponds to a particular gauge of the underlying symmetry, there is a web of dualities relating them. The dualities between said systems amount to canonical transformations including time and energy, which allows the different systems to be described by different Hamiltonians, and consequently, to correspond to different dynamics in the (d -- 1)+1 phase space. The second context, corresponds to a Weyl invariant scalar-tensor theory of gravity, obtained as a direct prediction of 2T gravity, where the Weyl symmetry is used to obtain geodesically complete dynamics both in the context of cosmology and black hole (BH) backgrounds. The geodesic incompleteness of usual Einstein gravity, in the presence of singularities in spacetime, is related to the definition of the Einstein gauge, which fixes the sign and magnitude of the gravitational constant GN, and therefore misses the existence of antigravity patches, which are expected to arise generically just beyond gravitational singularities. The definition of the Einstein gauge can be generalized by incorporating a sign flip of the gravitational constant GN at the transitions between gravity and antigravity. This sign is a key aspect that allows us to define geodesically complete dynamics in cosmology and in BH backgrounds, particularly, in the case of the 4D Schwarzschild BH and the 2D stringy BH. The complete nature of particle geodesics in these BH backgrounds is exhibited explicitly at the classical level, and the extension of these results to the

Newtonian potential and geodesic completeness in infinite derivative gravity

Science.gov (United States)

Edholm, James; Conroy, Aindriú

2017-08-01

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

Singularities in geodesic surface congruence

International Nuclear Information System (INIS)

Cho, Yong Seung; Hong, Soon-Tae

2008-01-01

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

The scalar wave equation in a Schwarzschild space-time

International Nuclear Information System (INIS)

Schmidt, B.G.; Stewart, J.M.

1979-01-01

This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild space-time in a neighbourhood of spatial infinity which includes parts of future and pass null infinity. The behaviour of such fields is essentially different from that which occurs in a flat space-time. In particular fields which have a Bondi-type expansion in powers of 'r(-1)' near past null infinity do not have such an expansion near future null infinity. Further solutions which have physically reasonable Cauchy data probably fail to have Bondi-type expansions near null infinity. (author)

Ambitwistor strings at null infinity and (subleading) soft limits

International Nuclear Information System (INIS)

Geyer, Yvonne; Lipstein, Arthur E; Mason, Lionel

2015-01-01

The relationship between BMS symmetries at null infinity and Weinberg's soft theorems for gravitons and photons together with their subleading extensions are developed using ambitwistor string theory. Ambitwistor space is the phase space of complex null geodesics in complexified space-time. We show how it can be canonically identified with the cotangent bundle of complexified null infinity. BMS symmetries of null infinity lift to give a Hamiltonian action on ambitwistor space, both in general dimension and in its twistorial four-dimensional representation. General vertex operators arise from Hamiltonians generating diffeomorphisms of ambitwistor space that determine the scattering from past to future null infinity. When a momentum eigenstate goes soft, the diffeomorphism defined by its leading and its subleading part are extended BMS generators realized in the world sheet conformal field theory of the ambitwistor string. More generally, this gives an explicit perturbative correspondence between the scattering of null geodesics and that of the gravitational field via ambitwistor string theory. (paper)

Note on cosmic censorship

International Nuclear Information System (INIS)

Tipler, F.J.

1985-01-01

A number of recent theorems by Krolak and Newman purport to prove cosmic censorship by showing that ''strong curvature'' singularities must be hidden behind horizons. It is proved that Newman's ''null, strong curvature'' condition, which is imposed on certain classes of null geodesics to restrict curvature growth in the space-time, does not hold in many physically realistic space-times: it is not satisfied by any null geodesic in the relevant class in any open Friedmann cosmological model, nor does it hold for any null geodesic in the relevant class in maximal Schwarzschild space. More generally, it is argued that the singularity predicted by the Penrose singularity theorem is unlikely to be of the type eliminated by Newman. Thus the Newman theorems are probably without physical significance. The Krolak theorems, although based on a physically significant definition of strong curvature singularity, are mathematically invalid, and this approach cannot be used to obtain a cosmic censorship theorem. (author)

Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

Science.gov (United States)

Kassandrov, Vladimir V.; Rizcallah, Joseph A.

We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.

Focusing of geodesic congruences in an accelerated expanding Universe

International Nuclear Information System (INIS)

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

2012-01-01

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

Focusing of geodesic congruences in an accelerated expanding Universe

Energy Technology Data Exchange (ETDEWEB)

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

2012-12-01

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

Geodesics and symmetries of doubly spinning black rings

International Nuclear Information System (INIS)

Durkee, Mark

2009-01-01

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

The scalar wave equation in a Schwarzschild spacetime

International Nuclear Information System (INIS)

Stewart, J.M.; Schmidt, B.G.

1978-09-01

This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild spacetime in a neighbourhood of spatial infinity, which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which accurs in a flat spacetime. (orig.) [de

Spacetime completeness of non-singular black holes in conformal gravity

Energy Technology Data Exchange (ETDEWEB)

Bambi, Cosimo; Rachwał, Lesław [Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai (China); Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com [Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Road, Shenzhen 518055 (China)

2017-05-01

We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new types of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r =0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.

From GLC to double-null coordinates and illustration with static black holes

Energy Technology Data Exchange (ETDEWEB)

Nugier, Fabien, E-mail: fnugier@ntu.edu.tw [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617 Taiwan (China)

2016-09-01

We present a system of coordinates deriving directly from the so-called Geodesic Light-Cone (GLC) coordinates and made of two null scalars intersecting on a 2-dimensional sphere parameterized by two constant angles along geodesics. These coordinates are shown to be equivalent to the well-known double-null coordinates. As GLC, they present interesting properties for cosmology and astrophysics. We discuss this latter topic for static black holes, showing simple descriptions for the metric or particles and photons trajectories. We also briefly comment on the time of flight of ultra-relativistic particles.

Averaged null energy condition and difference inequalities in quantum field theory

International Nuclear Information System (INIS)

Yurtsever, U.

1995-01-01

For a large class of quantum states, all local (pointwise) energy conditions widely used in relativity are violated by the renormalized stress-energy tensor of a quantum field. In contrast, certain nonlocal positivity constraints on the quantum stress-energy tensor might hold quite generally, and this possibility has received considerable attention in recent years. In particular, it is now known that the averaged null energy condition, the condition that the null-null component of the stress-energy tensor integrated along a complete null geodesic is non-negative for all states, holds quite generally in a wide class of spacetimes for a minimally coupled scalar field. Apart from the specific class of spacetimes considered (mainly two-dimensional spacetimes and four-dimensional Minkowski space), the most significant restriction on this result is that the null geodesic over which the average is taken must be achronal. Recently, Ford and Roman have explored this restriction in two-dimensional flat spacetime, and discovered that in a flat cylindrical space, although the stress energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (nonachronal) null geodesics, when the ''Casimir-vacuum'' contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ''difference inequalities.'' Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary (globally hyperbolic) two-dimensional spacetime, using the same techniques as those we relied on to prove the ANEC in an earlier paper with Wald. I begin with an overview of averaged energy conditions in quantum field theory

Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

Science.gov (United States)

Rodrigue, Kamiko Kouemeni Jean; Saleh, Mahamat; Thomas, Bouetou Bouetou; Kofane, Timoleon Crepin

2018-05-01

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh-Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein-Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter (ρ 0) were explicitly plotted. The results show that, when the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter at r=1 (ρ 0) vanish (ρ 0=ɛ =0), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing ρ 0, the transition points are shifted to lower entropies. The same thing is observed when increasing ɛ 2. In the absence of quintessence-like matter (ρ 0=0), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing ρ 0 or (ɛ ^2).

On smoothness-asymmetric null infinities

International Nuclear Information System (INIS)

Valiente Kroon, Juan Antonio

2006-01-01

We discuss the existence of asymptotically Euclidean initial data sets for the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (nonlinearly) distorted Schwarzschild black hole. Their developments would be that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity

Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

Energy Technology Data Exchange (ETDEWEB)

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

2016-11-25

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

Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

International Nuclear Information System (INIS)

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

2016-01-01

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

The effect of spherical shells of matter on the Schwarzschild black hole

International Nuclear Information System (INIS)

Dray, T.; Rijksuniversiteit Utrecht; Hooft, G. 't

1985-01-01

Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce spacetimes with a C 0 metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational ''shock waves'' at the horizon of a Schwarzschild black hole, and (2) a configuration involving only one external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the ''Wheeler wormhole'' to another universe. (orig.)

From geodesics of the multipole solutions to the perturbed Kepler problem

International Nuclear Information System (INIS)

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

2010-01-01

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

Geodesic patterns

KAUST Repository

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

2010-01-01

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

Geodesic patterns

KAUST Repository

Pottmann, Helmut

2010-07-26

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

Can geodesics in extra dimensions solve the cosmological horizon problem?

International Nuclear Information System (INIS)

Chung, Daniel J. H.; Freese, Katherine

2000-01-01

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

The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

OpenAIRE

Johnson, Thomas

2018-01-01

In a recent seminal paper \\cite{D--H--R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solutions to the Einstein vacuum equations by imposing instead a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the...

Geometric extension through Schwarzschild r = 0

International Nuclear Information System (INIS)

Lynden-Bell, D.; Katz, J.; Hebrew Univ., Jerusalem

1990-01-01

Singularities in space-time are not necessarily cancers in the manifold but can herald interesting topological change in the space-time at places where there are several different tangent Minkowski spaces. Most discussions of gravitational collapse cease when space-time becomes singular. In the 'hour-glass' universe we have an example where the singularity develops in empty space; here we give a geometrical extension through the singularity in which geodesics that enter it emerge into a new space. The result extends Schwarzschild space and is periodic in 'extended' Penrose coordinates. There is a topological singularity but no mass at r = 0. The extension is mildly nonanalytic but unique. It is based on the concept that time does not stop and that empty space-times which develop singularities must still have zero Ricci tensors even where the Riemann tensor becomes infinite. (author)

Shearfree congruences of null geodesics and Killing tensors

International Nuclear Information System (INIS)

Dietz, W.; Ruediger, R.

1980-01-01

In this communication, the mutual connections between quantities that are generalizations of the notion of a a Killing vector field are investigated. A classification of these quantities in terms of a complex vector field αsub(a) is given. A common feature of all these quantities is that they imply the existence of a pair of shearfree geodetic null congruences. There are no explicit restrictions posed on the Ricci tensor. (author)

Doppler frequency in interplanetary radar and general relativity

Science.gov (United States)

Mcvittie, G. C.

1972-01-01

The change of frequency of an interplanetary radar signal sent from the earth to another planet or to a space probe is worked out according to general relativity. The Schwarzschild spacetime is employed and its null geodesics control the motion of the signals. Exact Doppler frequency formulas are derived for one-way and two-way radar in terms of an arbitrary Schwarzschild radial coordinate. A reduction to the special relativity case is used to interpret the formulas in terms of the relative radial velocity of emitter and target. The general relativity corrections are worked out approximately for each of three possible Schwarzschild radial coordinates, and a numerical example is given. The amount of the correction is different according as one or the other of the Schwarzschild coordinates is identified with the radius vector deduced from classical celestial mechanics. The identification problem is discussed.

Traversable Schwarzschild-like wormholes

Energy Technology Data Exchange (ETDEWEB)

Cataldo, Mauricio [Universidad del Bio-Bio, Departamento de Fisica, Facultad de Ciencias, Concepcion (Chile); Grupo de Cosmologia y Gravitacion-UBB, Concepcion (Chile); Liempi, Luis [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Universidad San Sebastian, Facultad de Ingenieria y Tecnologia, Concepcion (Chile); Rodriguez, Pablo [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile)

2017-11-15

In this paper we study relativistic static traversable wormhole solutions which are a slight generalization of Schwarzschild wormholes. In order to do this we assume a shape function with a linear dependence on the radial coordinate r. This linear shape function generates wormholes whose asymptotic spacetime is not flat: they are asymptotically locally flat, since in the asymptotic limit r → ∞ spacetimes exhibiting a solid angle deficit (or excess) are obtained. In particular, there exist wormholes which connect two asymptotically non-flat regions with a solid angle deficit. For these wormholes the size of their embeddings in a three-dimensional Euclidean space extends from the throat to infinity. A new phantom zero-tidal-force wormhole exhibiting such asymptotic is obtained. On the other hand, if a solid angle excess is present, the size of the wormhole embeddings depends on the amount of this angle excess, and the energy density is negative everywhere. We discuss the traversability conditions and study the impact of the β-parameter on the motion of a traveler when the wormhole throat is crossed. A description of the geodesic behavior for the wormholes obtained is also presented. (orig.)

Traversable Schwarzschild-like wormholes

International Nuclear Information System (INIS)

Cataldo, Mauricio; Liempi, Luis; Rodriguez, Pablo

2017-01-01

In this paper we study relativistic static traversable wormhole solutions which are a slight generalization of Schwarzschild wormholes. In order to do this we assume a shape function with a linear dependence on the radial coordinate r. This linear shape function generates wormholes whose asymptotic spacetime is not flat: they are asymptotically locally flat, since in the asymptotic limit r → ∞ spacetimes exhibiting a solid angle deficit (or excess) are obtained. In particular, there exist wormholes which connect two asymptotically non-flat regions with a solid angle deficit. For these wormholes the size of their embeddings in a three-dimensional Euclidean space extends from the throat to infinity. A new phantom zero-tidal-force wormhole exhibiting such asymptotic is obtained. On the other hand, if a solid angle excess is present, the size of the wormhole embeddings depends on the amount of this angle excess, and the energy density is negative everywhere. We discuss the traversability conditions and study the impact of the β-parameter on the motion of a traveler when the wormhole throat is crossed. A description of the geodesic behavior for the wormholes obtained is also presented. (orig.)

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

Science.gov (United States)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation

Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring

Science.gov (United States)

Basovník, M.; Semerák, O.

2016-08-01

We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.

Upper bound on the radii of black-hole photonspheres

International Nuclear Information System (INIS)

Hod, Shahar

2013-01-01

One of the most remarkable predictions of the general theory of relativity is the existence of black-hole “photonspheres”, compact null hypersurfaces on which massless particles can orbit the central black hole. We prove that every spherically-symmetric asymptotically flat black-hole spacetime is characterized by a photonsphere whose radius is bounded from above by r γ ⩽3M, where M is the total ADM mass of the black-hole spacetime. It is shown that hairy black-hole configurations conform to this upper bound. In particular, the null circular geodesic of the (bald) Schwarzschild black-hole spacetime saturates the bound

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

Science.gov (United States)

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

2014-07-01

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

Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications

Science.gov (United States)

Arakida, Hideyoshi

2018-05-01

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.

Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes

OpenAIRE

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...

Martin Schwarzschild (1912 - 1997)

Science.gov (United States)

Pfau, Werner

The Chairman of the Astronomische Gesellschaft honored Martin Schwarzschild, who was the first to be presented with the Karl Schwarzschild Medal of the Astronomische Gesellschaft in 1957. An account of his life and work is given.

Plate with a hole obeys the averaged null energy condition

International Nuclear Information System (INIS)

Graham, Noah; Olum, Ken D.

2005-01-01

The negative energy density of Casimir systems appears to violate general relativity energy conditions. However, one cannot test the averaged null energy condition (ANEC) using standard calculations for perfectly reflecting plates, because the null geodesic would have to pass through the plates, where the calculation breaks down. To avoid this problem, we compute the contribution to ANEC for a geodesic that passes through a hole in a single plate. We consider both Dirichlet and Neumann boundary conditions in two and three space dimensions. We use a Babinet's principle argument to reduce the problem to a complementary finite disk correction to the perfect mirror result, which we then compute using scattering theory in elliptical and spheroidal coordinates. In the Dirichlet case, we find that the positive correction due to the hole overwhelms the negative contribution of the infinite plate. In the Neumann case, where the infinite plate gives a positive contribution, the hole contribution is smaller in magnitude, so again ANEC is obeyed. These results can be extended to the case of two plates in the limits of large and small hole radii. This system thus provides another example of a situation where ANEC turns out to be obeyed when one might expect it to be violated

On the geometry of null cones to infinity under curvature flux bounds

International Nuclear Information System (INIS)

Alexakis, Spyros; Shao, Arick

2014-01-01

The main objective of this paper is to control the geometry of a future outgoing truncated null cone extending smoothly toward infinity in an Einstein-vacuum spacetime. In particular, we wish to do this under minimal regularity assumptions, namely, at the (weighted) L 2 -curvature level. We show that if the curvature flux and the data on an initial sphere of the cone are sufficiently close to the corresponding values in a standard Minkowski or Schwarzschild null cone, then we can obtain quantitative bounds on the geometry of the entire infinite cone. The same bounds also imply the existence of limits at infinity, along the null cone, of naturally scaled geometric quantities. In Alexakis and Shao (2013 Bounds on the Bondi energy by a flux of curvature arXiv:1308.4170), we will apply these results in order to control various physical quantities—e.g., the Bondi energy and (linear and angular) momenta—associated with such infinite null cones in vacuum spacetimes. (paper)

Statistics of geodesics in large quadrangulations

International Nuclear Information System (INIS)

Bouttier, J; Guitter, E

2008-01-01

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

Exact geodesic distances in FLRW spacetimes

Science.gov (United States)

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

2017-11-01

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

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

Science.gov (United States)

Stuchlík, Zdeněk; Schee, Jan

2015-12-01

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

On geodesics in low regularity

Science.gov (United States)

Sämann, Clemens; Steinbauer, Roland

2018-02-01

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

Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism

International Nuclear Information System (INIS)

Martel, Karl; Poisson, Eric

2005-01-01

We present a formalism to study the metric perturbations of the Schwarzschild spacetime. The formalism is gauge invariant, and it is also covariant under two-dimensional coordinate transformations that leave the angular coordinates unchanged. The formalism is applied to the typical problem of calculating the gravitational waves produced by material sources moving in the Schwarzschild spacetime. We examine the radiation escaping to future null infinity as well as the radiation crossing the event horizon. The waveforms, the energy radiated, and the angular-momentum radiated can all be expressed in terms of two gauge-invariant scalar functions that satisfy one-dimensional wave equations. The first is the Zerilli-Moncrief function, which satisfies the Zerilli equation, and which represents the even-parity sector of the perturbation. The second is the Cunningham-Price-Moncrief function, which satisfies the Regge-Wheeler equation, and which represents the odd-parity sector of the perturbation. The covariant forms of these wave equations are presented here, complete with covariant source terms that are derived from the stress-energy tensor of the matter responsible for the perturbation

Schwarzschild, Martin (1912-97)

Science.gov (United States)

Murdin, P.

2000-11-01

Astrophysicist, born in Potsdam, Germany, the son of KARL SCHWARZSCHILD, left Germany, became professor at Princeton University. Working with John von Neumann, Schwarzschild used the powers of the newly developed electronic digital computers to work on the theory of stellar structure and evolution. He uncovered phenomena in red giant stars, including how they evolve off the main sequence in the H...

Equatorial Geodesics Around the Magnetars

Science.gov (United States)

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

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

Geodesics in (Rn, d1

Directory of Open Access Journals (Sweden)

Mehmet KILIÇ

2016-09-01

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

Two-mirror Schwarzschild aplanats. Basic relations

OpenAIRE

Terebizh, V. Yu.

2005-01-01

It is shown that the theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 leads to the unified description both the prefocal and the postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chretien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at fast focal ...

Two-Mirror Schwarzschild Aplanats: Basic Relations

Science.gov (United States)

Terebizh, V. Yu.

2005-02-01

The theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 is shown to lead to a unified description of both prefocal and postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chrétien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at the system’s fast focal ratio.

Diffeomorphometry and geodesic positioning systems for human anatomy.

Science.gov (United States)

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

2014-03-01

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

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

Geodesics in thermodynamic state spaces of quantum gases

International Nuclear Information System (INIS)

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

2002-01-01

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

Pair of null gravitating shells: III. Algebra of Dirac's observables

International Nuclear Information System (INIS)

Kouletsis, I; Hajicek, P

2002-01-01

The study of the two-shell system started in 'pair of null gravitating shells I and II' is continued. The pull back of the Liouville form to the constraint surface, which contains complete information about the Poisson brackets of Dirac observables, is computed in the singular double-null Eddington-Finkelstein (DNEF) gauge. The resulting formula shows that the variables conjugate to the Schwarzschild masses of the intershell spacetimes are simple combinations of the values of the DNEF coordinates on these spacetimes at the shells. The formula is valid for any number of in- and outgoing shells. After applying it to the two-shell system, the symplectic form is calculated for each component of the physical phase space; regular coordinates are found, defining it as a symplectic manifold. The symplectic transformation between the initial and final values of observables for the shell-crossing case is given

Congruences of totally geodesic surfaces

International Nuclear Information System (INIS)

Plebanski, J.F.; Rozga, K.

1989-01-01

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

Geodesic exponential kernels: When Curvature and Linearity Conflict

DEFF Research Database (Denmark)

Feragen, Aase; Lauze, François; Hauberg, Søren

2015-01-01

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

On certain geodesic conjugacies of flat cylinders

Indian Academy of Sciences (India)

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

Geodesic distance in planar graphs

International Nuclear Information System (INIS)

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

2003-01-01

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

Generating geodesic flows and supergravity solutions

NARCIS (Netherlands)

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

2009-01-01

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

Craniofacial Reconstruction Evaluation by Geodesic Network

Directory of Open Access Journals (Sweden)

Junli Zhao

2014-01-01

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

Efficiently computing exact geodesic loops within finite steps.

Science.gov (United States)

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

2012-06-01

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

A regularized approach for geodesic-based semisupervised multimanifold learning.

Science.gov (United States)

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

2014-05-01

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

Initial data sets for the Schwarzschild spacetime

International Nuclear Information System (INIS)

Gomez-Lobo, Alfonso Garcia-Parrado; Kroon, Juan A. Valiente

2007-01-01

A characterization of initial data sets for the Schwarzschild spacetime is provided. This characterization is obtained by performing a 3+1 decomposition of a certain invariant characterization of the Schwarzschild spacetime given in terms of concomitants of the Weyl tensor. This procedure renders a set of necessary conditions--which can be written in terms of the electric and magnetic parts of the Weyl tensor and their concomitants--for an initial data set to be a Schwarzschild initial data set. Our approach also provides a formula for a static Killing initial data set candidate--a KID candidate. Sufficient conditions for an initial data set to be a Schwarzschild initial data set are obtained by supplementing the necessary conditions with the requirement that the initial data set possesses a stationary Killing initial data set of the form given by our KID candidate. Thus, we obtain an algorithmic procedure of checking whether a given initial data set is Schwarzschildean or not

Schwarzschild Solution: A Historical Perspective

Science.gov (United States)

Bartusiak, Marcia

2016-03-01

While eighteenth-century Newtonians had imagined a precursor to the black hole, the modern version has its roots in the first full solution to Einstein's equations of general relativity, derived by the German astronomer Karl Schwarzschild on a World War I battlefront just weeks after Einstein introduced his completed theory in November 1915. This talk will demonstrate how Schwarzschild's solution is linked to the black hole and how it took more than half a century for the physics community to accept that such a bizarre celestial object could exist in the universe.

Higher-order geodesic deviations applied to the Kerr metric

CERN Document Server

Colistete, R J; Kerner, R

2002-01-01

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

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

International Nuclear Information System (INIS)

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

1988-10-01

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

Symmetries and conserved quantities in geodesic motion

International Nuclear Information System (INIS)

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

1986-01-01

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

Singular Null Hypersurfaces in General Relativity

International Nuclear Information System (INIS)

Dray, T

2006-01-01

test particles in such a spacetime, in an initial attempt to outline a framework for the detection of impulsive gravitational waves. Subsequent chapters describe the singular null hypersurfaces obtained by boosting isolated gravitational sources, building on the work of Aichelburg and Sexl, and by colliding impulsive waves, building on the work of Khan and Penrose. In between, the special case of spherical symmetry is considered, both with and without collisions. There is also a short chapter discussing the effect of replacing GR by alternative theories of gravity, and an appendix which briefly summarizes the non-null case. The references are reasonably complete, from Synge and Penrose to the recent work of the authors. However, there are a few relatively minor errors and omissions. For instance, the results in chapter 3 about shells of matter in both Schwarzschild and Reissner-Nordstroem geometries are presented without reference or derivation. And I was disappointed to see that my own work with 't Hooft on the horizon shift due to the impulsive wave of a massless particle at the horizon of a Schwarzschild black hole-a direct generalization of the work by Aichelburg and Sexl-is not mentioned. But none of these minor complaints detracts from my appreciation of having a complete discussion of singular null hypersurfaces all in one place. The three fundamental papers which started this area of research all appeared at essentially the same time, 35 years ago; it is high time there was a unified presentation of the entire field. This book fills that need admirably, and could serve as the core of a graduate seminar for students having already taken a course in general relativity, or as a reference. My copy will have a treasured place in my library. References Penrose R 1972 The geometry of impulsive gravitational waves General Relativity: Papers in Honour of J L Synge ed L O Raifeartaigh (Oxford: Clarendon) pp 101-30 Aichelburg P C and Sexl R U 1971 On the gravitational

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Craniofacial Reconstruction Evaluation by Geodesic Network

OpenAIRE

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

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Sheng-lan Chen

2014-01-01

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

Geodesic motion and confinement in Goedel's universe

International Nuclear Information System (INIS)

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

1982-01-01

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

Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics

Directory of Open Access Journals (Sweden)

Liandong Zhang

2012-01-01

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

Instantons from geodesics in AdS moduli spaces

Science.gov (United States)

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

2018-03-01

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

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.

The Schwarzschild metric: It's the coordinates, stupid!

Science.gov (United States)

Fromholz, Pierre; Poisson, Eric; Will, Clifford M.

2014-04-01

Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation that is simple and one that is a mess. We give a concrete illustration of the maxim that "coordinates matter" using the exact Schwarzschild solution for a vacuum, static spherical spacetime. We review the standard textbook derivation, Schwarzschild's original 1916 derivation, and a derivation using the Landau-Lifshitz formulation of the Einstein field equations. The last derivation is much more complicated, has one aspect for which we have been unable to find a solution, and gives an explicit illustration of the fact that the Schwarzschild geometry can be described in infinitely many coordinate systems.

Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

Science.gov (United States)

Sharif, M.; Kousar, Lubna

2018-03-01

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordström black hole. We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles. We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole. The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole. The radial geodesic component starts decreasing in dyonic Reissner-Nordström black hole unlike Schwarzschild case. We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.

The Kerr/fluid duality and the singularity of solutions to the fluid equation

International Nuclear Information System (INIS)

Fujisawa, Ippei; Nakayama, Ryuichi

2016-01-01

An equation for a viscous incompressible fluid on a spheroidal surface that is dual to the perturbation around the near-near-horizon extreme Kerr (near-NHEK) black hole is derived. It is also shown that an expansion scalar θ of a congruence of null geodesics on the perturbed horizon of the perturbed near-NHEK spacetime, which is dual to a viscous incompressible fluid, is not in general positive semidefinite, even if initial conditions on the velocity are smooth. Unless the initial conditions are appropriately adjusted, caustics of null congruence will occur on the perturbed horizon in the future. A similar result is obtained for a perturbed Schwarzschild black hole spacetime, which is dual to a viscous incompressible fluid on S 2 . An initial condition that θ be positive semidefinite at any point on S 2 is a necessary condition for the existence of smooth solutions to the incompressible Navier-Stokes equation on S 2

Geodesic detection of Agulhas rings

Science.gov (United States)

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

2012-12-01

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

Analytic extension of the Schwarzschild-de Sitter metric

International Nuclear Information System (INIS)

Bazanski, S.L.; Ferrari, V.

1986-01-01

In this paper, co-ordinates are derived that are regular, respectively, in the neighbourhood of the two horizons which exist in the so-called Schwarzschild-de Sitter solution known in general relativity, and it is constructed a manifold that is the analytic extension of the manifold being the domain of classical Schwarzschild-de Sitter co-ordinates

Structure of the effective potential for a spherical wormhole

International Nuclear Information System (INIS)

Montelongo Garcia, N.; Zannias, T.

2008-01-01

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

The geometry of geodesics

CERN Document Server

Busemann, Herbert

2005-01-01

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

The self-force on a non-minimally coupled static scalar charge outside a Schwarzschild black hole

International Nuclear Information System (INIS)

Cho, Demian H J; Tsokaros, Antonios A; Wiseman, Alan G

2007-01-01

The finite part of the self-force on a static, non-minimally coupled scalar test charge outside a Schwarzschild black hole is zero. This result is determined from the work required to slowly raise or lower the charge through an infinitesimal distance. Unlike similar force calculations for minimally-coupled scalar charges or electric charges, we find that we must account for a flux of field energy that passes through the horizon and changes the mass and area of the black hole when the charge is displaced. This occurs even for an arbitrarily slow displacement of the non-minimally coupled scalar charge. For a positive coupling constant, the area of the hole increases when the charge is lowered and decreases when the charge is raised. The fact that the self-force vanishes for a static, non-minimally coupled scalar charge in Schwarzschild spacetime agrees with a simple prediction of the Quinn-Wald axioms. However, Zel'nikov and Frolov computed a non-vanishing self-force for a non-minimally coupled charge. Our method of calculation closely parallels the derivation of Zel'nikov and Frolov, and we show that their omission of this unusual flux is responsible for their (incorrect) result. When the flux is accounted for, the self-force vanishes. This correction eliminates a potential counter example to the Quinn-Wald axioms. The fact that the area of the black hole changes when the charge is displaced brings up two interesting questions that did not arise in similar calculations for static electric charges and minimally coupled scalar charges. (1) How can we reconcile a decrease in the area of the black hole horizon with the area theorem which concludes that δArea horizon ≥ 0? The key hypothesis of the area theorem is that the stress-energy tensor must satisfy a null-energy condition T αβ l α l β ≥ 0 for any null vector l α . We explicitly show that the stress-energy associated with a non-minimally coupled field does not satisfy this condition, and this violation of

Lorentz violation and black-hole thermodynamics

International Nuclear Information System (INIS)

Betschart, G.; Kant, E.; Klinkhamer, F.R.

2009-01-01

We consider nonstandard photons from nonbirefringent modified Maxwell theory and discuss their propagation in a fixed Schwarzschild spacetime background. This particular modification of Maxwell theory is Lorentz-violating and allows for maximal photon velocities differing from the causal speed c of the asymptotic background spacetime. In the limit of geometrical optics, light rays from modified Maxwell theory are found to propagate along null geodesics in an effective metric. We observe that not every Lorentz-violating theory with multiple maximal velocities different from the causal speed c modifies the notion of the event horizon, contrary to naive expectations. This result implies that not every Lorentz-violating theory with multiple maximal velocities necessarily leads to a contradiction with the generalized second law of thermodynamics.

Quantum corrections to Schwarzschild black hole

Energy Technology Data Exchange (ETDEWEB)

Calmet, Xavier; El-Menoufi, Basem Kamal [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)

2017-04-15

Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein's gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a non-local effective action. We work to quadratic order in curvatures simultaneously taking local and non-local corrections into account. Looking for solutions perturbatively close to that of classical general relativity, we find that an eternal Schwarzschild black hole remains a solution and receives no quantum corrections up to this order in the curvature expansion. In contrast, the field of a massive star receives corrections which are fully determined by the effective field theory. (orig.)

Heuristic extension of the Schwarzschild metric

International Nuclear Information System (INIS)

Espinosa, J.M.

1982-01-01

The Schwarzschild solution of Einstein's equations of gravitation has several singularities. It is known that the singularity at r = 2Gm/c 2 is only apparent, a result of the coordinates in which the solution was found. Paradoxical results occuring near the singularity show the system of coordinates is incomplete. We introduce a simple, two-dimensional metric with an apparent singularity that makes it incomplete. By a straightforward, heuristic procedure we extend and complete this simple metric. We then use the same procedure to give a heuristic derivation of the Kruskal system of coordinates, which is known to extend the Schwarzschild manifold past its apparent singularity and produce a complete manifold

Geodesic congruences in the Palatini f(R) theory

International Nuclear Information System (INIS)

Shojai, Fatimah; Shojai, Ali

2008-01-01

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

Exact optics - III. Schwarzschild's spectrograph camera revised

Science.gov (United States)

Willstrop, R. V.

2004-03-01

Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.

Non-integrability of geodesic flow on certain algebraic surfaces

International Nuclear Information System (INIS)

Waters, T.J.

2012-01-01

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

1st Karl Schwarzschild Meeting on Gravitational Physics

CERN Document Server

Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus

2016-01-01

These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the 140th anniversary of Schwarzschild's birth. They are grouped into 4 main themes: I. The Life and Work of Karl Schwarzschild; II. Black Holes in Classical General Relativity, Numerical Relativity, Astrophysics, Cosmology, and Alternative Theories of Gravity; III. Black Holes in Quantum Gravity and String Theory; IV. Other Topics in Contemporary Gravitation. Inspired by the foundational principle ``By acknowledging the past, we open a route to the future",  the week-long meeting, envisioned as a forum for exchange between scientists from all locations and levels of education, drew participants from 15 countries across 4 continents. In addition to plenary talks from leading researchers, a special focus on young talent was provided, a feature underlined by the Springer Prize for the best student and junior presentations.

On quantum deformation of the Schwarzschild solution

International Nuclear Information System (INIS)

Kazakov, D.I.; Solodukhin, S.N.

1993-01-01

We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4 D theory of gravity with Einstein action reduces to the effective two-dimensional dilaton gravity. We have found that the Schwarzschild singularity at r=0 is shifted to the finite radius r min ∼ r PL , where the scalar curvature is finite, so that the space-time looks regular and consists of two asymptotically flat sheets glued at the hypersurface of constant radius. (author). 17 refs.; 4 figs

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

Statistical Entropy of Schwarzschild Black Holes

CERN Document Server

Englert, F

1998-01-01

The entropy of a seven dimensional Schwarzschild black hole of arbitrary large radius is obtained by a mapping onto a near extremal self-dual three-brane whose partition function can be evaluated. The three-brane arises from duality after submitting a neutral blackbrane, from which the Schwarzschild black hole can be obtained by compactification, to an infinite boost in non compact eleven dimensional space-time and then to a Kaluza-Klein compactification. This limit can be defined in precise terms and yields the Beckenstein-Hawking value up to a factor of order one which can be set to be exactly one with the extra assumption of keeping only transverse brane excitations. The method can be generalized to five and four dimensional black holes.

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

International Nuclear Information System (INIS)

Courdurier, Matias; Saez, Mariel

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

Ishikawa Goo

2015-06-01

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

Centennial of General Relativity (1915-2015); The Schwarzschild Solution and Black Holes

OpenAIRE

Blinder, S. M.

2015-01-01

This year marks the 100th anniversary of Einstein's General Theory of Relativity (1915-2015). The first nontrivial solution of the Einstein field equations was derived by Karl Schwarzschild in 1916. This Note will focus mainly on the Schwarzschild solution and the remarkable developments which it inspired, the most dramatic being the prediction of black holes. Later extensions of Schwarzschild's spacetime structure has led to even wilder conjectures, such as white holes and passages to other ...

Alternatives to Schwarzschild in the weak field limit of General Relativity

Energy Technology Data Exchange (ETDEWEB)

Bozza, V. [Dipartimento di Fisica ' E.R. Caianiello' , Università di Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (Italy); Postiglione, A., E-mail: valboz@sa.infn.it, E-mail: postiglione@fis.uniroma3.it [Dipartimento di Fisica ' E. Amaldi' , Università di Roma Tre, Via della Vasca Navale 84, 00149 Roma (Italy)

2015-06-01

The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match Schwarzschild asymptotically. On a phenomenological point of view, gravitational lensing in metrics falling as 1/r{sup q} has recently attracted great interest. In this work, we explore the conditions on the source matter for constructing static spherically symmetric metrics exhibiting an arbitrary power-law as Newtonian limit. For such space-times we also derive the expressions of gravitational redshift and force on probe masses, which, together with light deflection, can be used in astrophysical searches of non-Schwarzschild objects made up of exotic matter. Interestingly, we prove that even a minimally coupled scalar field with a power-law potential can support non-Schwarzschild metrics with arbitrary asymptotic behaviour.

Superintegrability of geodesic motion on the sausage model

Science.gov (United States)

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

2017-06-01

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

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

International Nuclear Information System (INIS)

Rowland, D R

2006-01-01

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

Optimized curve design for image analysis using localized geodesic distance transformations

Science.gov (United States)

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

2015-03-01

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

3D Facial Similarity Measure Based on Geodesic Network and Curvatures

Directory of Open Access Journals (Sweden)

Junli Zhao

2014-01-01

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

Quantum field theory in Schwarzschild and Rindler spaces

International Nuclear Information System (INIS)

Boulware, D.G.

1975-01-01

The problem of defining a scalar quantum field in the space-times described by the Schwarzschild and Rindler metrics is discussed. The matrix elements of the field operators are found by calculating the Green's functions for the fields. The requirement of positive frequencies for asymptotic timelike separations combined with a careful analysis of the continuity conditions at the event horizons yields a unique prescription for the Green's function. This in turn defines the vacuum state. In the Schwarzschild space the vacuum is shown to be stable and the lowest-energy state. In the Rindler space the quantization procedure yields the same results as quantization in Minkowski coordinates

Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

Directory of Open Access Journals (Sweden)

G. Abbas

2014-01-01

Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.

Quantitative properties of the Schwarzschild metric

Czech Academy of Sciences Publication Activity Database

Křížek, Michal; Křížek, Filip

2018-01-01

Roč. 2018, č. 1 (2018), s. 1-10 Institutional support: RVO:67985840 Keywords : exterior and interior Schwarzschild metric * proper radius * coordinate radius Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://astro.shu-bg.net/pasb/index_files/Papers/2018/SCHWARZ8.pdf

Circular orbits in cosmic string and Schwarzschild-AdS spacetime with Fermi-Walker transport

International Nuclear Information System (INIS)

Bakke, K.; Furtado, C.; Carvalho, A.M. de

2009-01-01

In this paper we discuss the Fermi-Walker transport of vectors along orbits in cosmic string and Schwarzschild-AdS spacetimes. We analyze the influence of acceleration on these holonomies. An effect similar to Thomas precession is observed within the process of Fermi-Walker transport along these circular orbits which are studied in the limit of vanishing cosmological constant in Schwarzschild-AdS case; also we obtain Fermi-Walker transport in a Schwarzschild background. In the case of a Schwarzschild spacetime, we analyze the quantized band holonomy invariance. In the limit of zero acceleration we recover the well-known results for holonomy matrix obtained by parallel transport in all these spacetimes. (orig.)

Some remarks on geodesics in gauge groups and harmonic maps

International Nuclear Information System (INIS)

Valli, G.

1987-08-01

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

Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution

Science.gov (United States)

Kotlařík, P.; Semerák, O.; Čížek, P.

2018-04-01

Will [Astrophys. J. 191, 521 (1974), 10.1086/152992] solved the perturbation of a Schwarzschild black hole due to a slowly rotating light concentric thin ring, using Green's functions expressed as infinite-sum expansions in multipoles and in the small mass and rotational parameters. In a previous paper [P. Čížek and O. Semerák, Astrophys. J. Suppl. Ser. 232, 14 (2017), 10.3847/1538-4365/aa876b], we expressed the Green functions in closed form containing elliptic integrals, leaving just summation over the mass expansion. Such a form is more practical for numerical evaluation, but mainly for generalizing the problem to extended sources where the Green functions have to be integrated over the source. We exemplified the method by computing explicitly the first-order perturbation due to a slowly rotating thin disc lying between two finite radii. After finding basic parameters of the system—mass and angular momentum of the black hole and of the disc—we now add further properties, namely those which reveal how the disc gravity influences geometry of the black-hole horizon and those of circular equatorial geodesics (specifically, radii of the photon, marginally bound and marginally stable orbits). We also realize that, in the linear order, no ergosphere occurs and the central singularity remains pointlike, and check the implications of natural physical requirements (energy conditions and subluminal restriction on orbital speed) for the single-stream as well as counter-rotating double-stream interpretations of the disc.

Surprising structures hiding in Penrose’s future null infinity

Science.gov (United States)

Newman, Ezra T.

2017-07-01

Since the late1950s, almost all discussions of asymptotically flat (Einstein-Maxwell) space-times have taken place in the context of Penrose’s null infinity, I+. In addition, almost all calculations have used the Bondi coordinate and tetrad systems. Beginning with a known asymptotically flat solution to the Einstein-Maxwell equations, we show first, that there are other natural coordinate systems, near I+, (analogous to light-cones in flat-space) that are based on (asymptotically) shear-free null geodesic congruences (analogous to the flat-space case). Using these new coordinates and their associated tetrad, we define the complex dipole moment, (the mass dipole plus i times angular momentum), from the l  =  1 harmonic coefficient of a component of the asymptotic Weyl tensor. Second, from this definition, from the Bianchi identities and from the Bondi-Sachs mass and linear momentum, we show that there exists a large number of results—identifications and dynamics—identical to those of classical mechanics and electrodynamics. They include, among many others, {P}=M{v}+..., {L}= {r} × {P} , spin, Newton’s second law with the rocket force term (\\dotM v) and radiation reaction, angular momentum conservation and others. All these relations take place in the rather mysterious H-space rather than in space-time. This leads to the enigma: ‘why do these well known relations of classical mechanics take place in H-space?’ and ‘What is the physical meaning of H-space?’

Geodesics in hypercomplex number systems. Application to commutative quaternions

International Nuclear Information System (INIS)

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

1997-10-01

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

Surfaces foliated by planar geodesics: a model forcurved wood design

DEFF Research Database (Denmark)

Brander, David; Gravesen, Jens

2017-01-01

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

Polyaffine parametrization of image registration based on geodesic flows

DEFF Research Database (Denmark)

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

2012-01-01

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

Un-graviton corrections to the Schwarzschild black hole

International Nuclear Information System (INIS)

Gaete, Patricio; Helayel-Neto, Jose A.; Spallucci, Euro

2010-01-01

We introduce an effective action smoothly extending the standard Einstein-Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original 'guess' of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and 'dressing' the Newtonian potential with un-gravitons, we solve the 'effective Einstein equations' including all order un-gravity effects. An unexpected 'bonus' of accounting un-gravity effects is the fractalisation of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension d U .

Wormholes minimally violating the null energy condition

Energy Technology Data Exchange (ETDEWEB)

Bouhmadi-López, Mariam [Departamento de Física, Universidade da Beira Interior, 6200 Covilhã (Portugal); Lobo, Francisco S N; Martín-Moruno, Prado, E-mail: mariam.bouhmadi@ehu.es, E-mail: fslobo@fc.ul.pt, E-mail: pmmoruno@fc.ul.pt [Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Edifício C8, 1749-016 Lisboa (Portugal)

2014-11-01

We consider novel wormhole solutions supported by a matter content that minimally violates the null energy condition. More specifically, we consider an equation of state in which the sum of the energy density and radial pressure is proportional to a constant with a value smaller than that of the inverse area characterising the system, i.e., the area of the wormhole mouth. This approach is motivated by a recently proposed cosmological event, denoted {sup t}he little sibling of the big rip{sup ,} where the Hubble rate and the scale factor blow up but the cosmic derivative of the Hubble rate does not [1]. By using the cut-and-paste approach, we match interior spherically symmetric wormhole solutions to an exterior Schwarzschild geometry, and analyse the stability of the thin-shell to linearized spherically symmetric perturbations around static solutions, by choosing suitable properties for the exotic material residing on the junction interface radius. Furthermore, we also consider an inhomogeneous generalization of the equation of state considered above and analyse the respective stability regions. In particular, we obtain a specific wormhole solution with an asymptotic behaviour corresponding to a global monopole.

A prescribing geodesic curvature problem

International Nuclear Information System (INIS)

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

1993-09-01

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

The stable problem of the black-hole connected region in the Schwarzschild black hole

OpenAIRE

Tian, Guihua

2005-01-01

The stability of the Schwarzschild black hole is studied. Using the Painlev\\'{e} coordinate, our region can be defined as the black-hole-connected region(r>2m, see text) of the Schwarzschild black hole or the white-hole-connected region(r>2m, see text) of the Schwarzschild black hole. We study the stable problems of the black-hole-connected region. The conclusions are: (1) in the black-hole-connected region, the initially regular perturbation fields must have real frequency or complex frequen...

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

Science.gov (United States)

Seriu, Masafumi

2015-10-01

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

The real meaning of complex Minkowski-space world-lines

Energy Technology Data Exchange (ETDEWEB)

Adamo, T M [University of Oxford, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB (United Kingdom); Newman, E T, E-mail: newman@pitt.ed [University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, PA 15213 (United States)

2010-04-07

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.

The real meaning of complex Minkowski-space world-lines

International Nuclear Information System (INIS)

Adamo, T M; Newman, E T

2010-01-01

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.

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

DEFF Research Database (Denmark)

Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole

2011-01-01

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

On Geodesic Exponential Kernels

DEFF Research Database (Denmark)

Feragen, Aasa; Lauze, François; Hauberg, Søren

2015-01-01

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

Curved spaces before Einstein: Karl Schwarzschild's cosmological speculations and the beginnings of relativistic cosmology (German Title: Gekrümmte Universen vor Einstein: Karl Schwarzschilds kosmologische Spekulationen und die Anfänge der relativistischen Kosmologie)

Science.gov (United States)

Schemmel, Matthias

In contrast to most of his collegues in astronomy and physics, the German astronomer Karl Schwarzschild immediately recognized the significance of general relativity for physics and astronomy, and played a pioneering role in its early development. In this contribution, it is argued that the clue for understanding Schwarzschild's exceptional reaction to general relativity lies in the study of his prerelativistic work. Long before the rise of general relativity, Schwarzschild occupied himself with foundational problems on the borderline of physics, astronomy, and mathematics that, from today's perspective, belong to the field of problems of that theory. In this contribution, the example of Schwarzschild's early speculations about the non-Euclidean nature of physical space on cosmological scales is presented and their reflection in his reception of general relativity is discussed.

Hawking radiation from four-dimensional Schwarzschild black holes in M theory

International Nuclear Information System (INIS)

Das, S.R.; Mathur, S.D.; Ramadevi, P.

1999-01-01

Recently a method has been developed for relating four dimensional Schwarzschild black holes in M theory to near-extremal black holes in string theory with four charges, using suitably defined open-quotes boostsclose quotes and T dualities. We show that this method can be extended to obtain the emission rate of low energy massless scalars for the four dimensional Schwarzschild hole from the microscopic picture of radiation from the near extremal hole. copyright 1999 The American Physical Society

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

Directory of Open Access Journals (Sweden)

Kun-Lin Wu

2016-01-01

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

Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes

International Nuclear Information System (INIS)

Nagar, Alessandro; Rezzolla, Luciano

2005-01-01

The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this review is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of a Schwarzschild black-hole spacetime driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes. (topical review)

Geodesic structure of Lifshitz black holes in 2+1 dimensions

International Nuclear Information System (INIS)

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

2013-01-01

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

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

OpenAIRE

Rahmani, Faramarz; Golshani, Mehdi

2017-01-01

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

Scattering and absorption of electromagnetic waves by a Schwarzschild black hole

International Nuclear Information System (INIS)

Fabbri, R.

1975-01-01

The scattering and absorption of electromagnetic waves by a spherically symmetric nonrotating black hole is studied in the Schwarzschild background, by means of the known expansion of the modified Debye potentials in partial waves. The power reflection coefficients and the phase shifts of the partial waves are evaluated at both high and low frequencies. Then the scattering and absorption cross sections of the black hole are determined. It is shown that the black hole is almost unable to absorb electromagnetic waves when the wave length of the radiation is greater than the Schwarzschild radius

The Schwarzschild effect of the dosimetry film Kodak EDR 2.

Science.gov (United States)

Djouguela, A; Kollhoff, R; Rubach, A; Harder, D; Poppe, B

2005-11-07

The magnitude of the Schwarzschild effect or failure of the reciprocity law has been experimentally investigated for the dosimetry film EDR 2 from Kodak. When the dose rate applied to achieve a given dose was reduced by a factor of 12, the net optical density was reduced by up to 5%. The clinical importance of this effect is negligible as long as the films are calibrated at a value of the dose rate approximately representative of the dose rates occurring in the target volume, but in target regions of strongly reduced dose rate the Schwarzschild effect should be allowed for by a correction of the net optical density.

Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story

OpenAIRE

Weinstein, Galina

2014-01-01

On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations. Einstein's field equations cannot be solved in the general case, but can be solved in particular situations. The first to offer such an exact solution was Karl Schwarzschild. Schwarzschild found one line element, which satisfied the conditions imposed by Einstein...

Complex manifolds in relativity

International Nuclear Information System (INIS)

Flaherty, E.J. Jr.

1975-01-01

Complex manifold theory is applied to the study of certain problems in general relativity. The first half of the work is devoted to the mathematical theory of complex manifold. Then a brief review of general relativity is given. It is shown that any spacetime admits locally an almost Hermitian structure, suitably modified to be compatible with the indefinite metric of spacetime. This structure is integrable if and only if the spacetime admits two geodesic and shearfree null congruences, thus in particular if the spacetime is type D vacuum or electrified. The structure is ''half-integrable'' in a suitable sense if and only if the spacetime admits one geodesic and shearfree null congruence, thus in particular for all algebraically special vacuum spacetimes. Conditions for the modified Hermitian spacetime to be Kahlerian are presented. The most general metric for such a modified Kahlerian spacetime is found. It is shown that the type D vacuum and electrified spacetimes are conformally related to modified Kahlerian spacetimes by a generally complex conformal factor. These latter are shown to possess a very rich structure, including the existence of Killing tensors and Killing vectors. A new ''explanation'' of Newman's complex coordinate transformations is given. It is felt to be superior to previous ''explanations'' on several counts. For example, a physical interpretation in terms of a symmetry group is given. The existence of new complex coordinate transformations is established: Nt is shown that any type D vacuum spacetime is obtainable from either Schwarzschild spacetime or ''C'' spacetime by a complex coordinate transformation. Finally, some related topics are discussed and areas for future work are outlined. (Diss. Abstr. Int., B)

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-09-15

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

Taub-NUT spinless particles and Schwarzschild spinning particles

International Nuclear Information System (INIS)

Bini, D.; La Sapienza Univ., Rome

2005-01-01

The effect of a small gravitomagnetic monopole on (accelerated) circular orbits in the equatorial plane of the Taub-NUT space-time is compared to the corresponding (accelerated) orbits pushed slightly off the equatorial plane in the absence of the monopole (Schwarzschild space-time)

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

Quasinormal Modes of a Quantum-Corrected Schwarzschild Black ...

Indian Academy of Sciences (India)

Chunyan Wang

2017-11-27

Nov 27, 2017 ... Abstract. In this work, we investigate the electromagnetic perturbation around a quantum-corrected. Schwarzschild black hole. The complex frequencies of the quasinormal modes are evaluated by the third- order WKB approximation. The numerical results obtained showed that the complex frequencies ...

Features and stability analysis of non-Schwarzschild black hole in quadratic gravity

International Nuclear Information System (INIS)

Cai, Yi-Fu; Zhang, Hezi; Liu, Junyu; Cheng, Gong; Wang, Min

2016-01-01

Black holes are found to exist in gravitational theories with the presence of quadratic curvature terms and behave differently from the Schwarzschild solution. We present an exhaustive analysis for determining the quasinormal modes of a test scalar field propagating in a new class of black hole backgrounds in the case of pure Einstein-Weyl gravity. Our result shows that the field decay of quasinormal modes in such a non-Schwarzschild black hole behaves similarly to the Schwarzschild one, but the decay slope becomes much smoother due to the appearance of the Weyl tensor square in the background theory. We also analyze the frequencies of the quasinormal modes in order to characterize the properties of new back holes, and thus, if these modes can be the source of gravitational waves, the underlying theories may be testable in future gravitational wave experiments. We briefly comment on the issue of quantum (in)stability in this theory at linear order.

Adaptive geodesic transform for segmentation of vertebrae on CT images

Science.gov (United States)

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

2014-03-01

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

Lagrangian averaging with geodesic mean.

Science.gov (United States)

Oliver, Marcel

2017-11-01

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

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

Directory of Open Access Journals (Sweden)

Panou G.

2017-02-01

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

Gravitational nonminimally coupled electromagnetic fields: a possible solution to some idiosincrasies of Einstein-Maxwell theory

International Nuclear Information System (INIS)

Accioly, A.J.

1988-01-01

A theory of nonminimal coupling of electromagnetism and gravitation in the framework of Riomannian geometry is constructed. As a consequence the main difficulties concerning the Einstein-Maxwell theory are cleared away. The theory works as a kind of correction to the Einstein-Maxwell one for regions with strong curvature and for times much greater than the Planck time. A Reissner-Nordstroem-type solution is exhibited and comments are made on a parameter which somewhat resembles the ''Schwarzschild radius''. A mechanism of charge creation via nonminimal coupling is also discussed. We calculate the propagation of photons in a Robertson-Walker background and find that the effect of the nonminimal coupling in this case may be to deviate the photon from the null geodesics, increasing its velocity beyond the flat-space value. Taking into account this results, the observed isotropy of the background radiation can be explained in a simple way, regardless of any assumption about the state of the Universe prior to the Planck time. (author) [pt

Collapsing radiating stars with various equations of state

Science.gov (United States)

Brassel, Byron P.; Goswami, Rituparno; Maharaj, Sunil D.

2017-06-01

We study the gravitational collapse of radiating stars in the context of the cosmic censorship conjecture. We consider a generalized Vaidya spacetime with three concentric regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. We outline the general mathematical framework to study the conditions on the mass function so that future-directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analyzed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities which implies that no extension of spacetime through them is possible.

On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

Directory of Open Access Journals (Sweden)

Oliver F. Piattella

2016-10-01

Full Text Available We analyse the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a point-like lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter, H, we derive and approximately solve the null geodesic equations, finding an expression for the bending angle δ, which we expand in powers of the mass-to-closest approach distance ratio and of the impact parameter-to-lens distance ratio. It turns out that the leading order of the aforementioned expansion is the same as the one calculated for the Schwarzschild metric and that cosmological corrections contribute to δ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of the H constant and find that they provide a correction of order 10−11 on the lens mass estimate.

Robinson manifolds and Cauchy-Riemann spaces

CERN Document Server

Trautman, A

2002-01-01

A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...

Constant scalar curvature hypersurfaces in extended Schwarzschild space-time

International Nuclear Information System (INIS)

Pareja, M. J.; Frauendiener, J.

2006-01-01

We present a class of spherically symmetric hypersurfaces in the Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are asymptotically flat

Karl Schwarzschild and the professionalization of astrophysics. (German Title: Karl Schwarzschild und die Professionalisierung der Astrophysik)

Science.gov (United States)

Schmidt-Kaler, Theodor

Professionalization is characteristic for physics and astronomy since 1830, and forms the basis for their rapid evolution in the 20th century. Karl Schwarzschild's contributions to professionalization of astronomy are presented: the introduction of course lectures in a repeating cycle, a permanent astrophysical laboratory, a tight connection between teaching and research, simulations and suggestions for astronomy at high schools and for the training of high school teachers, an interest in international organisation, and the initiative and planning of a southern observatory.

Three Göttingen lectures by Karl Schwarzschild, 1904-1905. (German Title: Drei Göttinger Vorlesungen Karl Schwarzschilds 1904-1905)

Science.gov (United States)

Schmidt-Kaler, Theodor

Karl Schwarzschild (1873-1916), perhaps the most eminent astronomer of his time, was professor at Göttingen University from 1901 to 1909. Three of his lectures from the years 1904 to 1906 are available in the form of copy-books written by his students Arnold Kohlschütter (1883-1969) and Max Born (1882-1970). Here, an overview of these lectures is given.

The Jacobi metric for timelike geodesics in static spacetimes

Science.gov (United States)

Gibbons, G. W.

2016-01-01

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

Classroom reconstruction of the Schwarzschild metric

OpenAIRE

Kassner, Klaus

2015-01-01

A promising way to introduce general relativity in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on differential geometry in its full glory and permits to emphasize physical aspects before attacking the field equations. Even so, in terms of motivation, lacking justification of the metric employed may pose an obstacle. The paper discusses how to establish the we...

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

Science.gov (United States)

Zaslavskii, O. B.

2015-03-01

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

Properties of an Arithmetic Code for Geodesic Flows

International Nuclear Information System (INIS)

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

2011-01-01

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

Generalized Fermat's principle and action for light rays in a curved spacetime

Science.gov (United States)

Frolov, Valeri P.

2013-09-01

We start with formulation of the generalized Fermat’s principle for light propagation in a curved spacetime. We apply Pontryagin’s minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a curved spacetime. We explicitly demonstrate that dynamical equations for this Hamiltonian correctly reproduce null geodesic equations. Other forms of the action for light rays in a curved spacetime are also discussed.

Distortion of Schwarzschild-anti-de Sitter black holes to black strings

International Nuclear Information System (INIS)

Tomimatsu, Akira

2005-01-01

Motivated by the existence of black holes with various topologies in four-dimensional spacetimes with a negative cosmological constant, we study axisymmetric static solutions describing any large distortions of Schwarzschild-anti-de Sitter black holes parametrized by the mass m. Under the approximation such that m is much larger than the anti-de Sitter radius, it is found that a cylindrically symmetric black string is obtained as a special limit of distorted spherical black holes. Such a prolonged distortion of the event horizon connecting a Schwarzschild-anti-de Sitter black hole to a black string is allowed without violating both the usual black hole thermodynamics and the hoop conjecture for the horizon circumference

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

Science.gov (United States)

2015-03-26

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

Asymptotic twistor theory and the Kerr theorem

International Nuclear Information System (INIS)

Newman, Ezra T

2006-01-01

We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds

Thermodynamic phase transition in the rainbow Schwarzschild black hole

International Nuclear Information System (INIS)

Gim, Yongwan; Kim, Wontae

2014-01-01

We study the thermodynamic phase transition in the rainbow Schwarzschild black hole where the metric depends on the energy of the test particle. Identifying the black hole temperature with the energy from the modified dispersion relation, we obtain the modified entropy and thermodynamic energy along with the modified local temperature in the cavity to provide well defined black hole states. It is found that apart from the conventional critical temperature related to Hawking-Page phase transition there appears an additional critical temperature which is of relevance to the existence of a locally stable tiny black hole; however, the off-shell free energy tells us that this black hole should eventually tunnel into the stable large black hole. Finally, we discuss the reason why the temperature near the horizon is finite in the rainbow black hole by employing the running gravitational coupling constant, whereas it is divergent near the horizon in the ordinary Schwarzschild black hole

Perfect fluid cosmology with geodesic world lines

International Nuclear Information System (INIS)

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

1978-01-01

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

Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions

Energy Technology Data Exchange (ETDEWEB)

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

2009-12-31

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

Gravitational lensing as a mechanism for effective cloaking

International Nuclear Information System (INIS)

Tippett, Benjamin K.

2011-01-01

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

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

Science.gov (United States)

Rahmani, Faramarz; Golshani, Mehdi

2018-01-01

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

Photon emission of extremal Kerr-Newman black holes

Energy Technology Data Exchange (ETDEWEB)

Wei, Shao-Wen; Gu, Bao-Min; Wang, Yong-Qiang; Liu, Yu-Xiao [Lanzhou University, Institute of Theoretical Physics, Lanzhou (China)

2017-02-15

In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr-Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained. (orig.)

Thermodynamics of the Schwarzschild and the Reissner–Nordström black holes with quintessence

Directory of Open Access Journals (Sweden)

K. Ghaderi

2016-02-01

Full Text Available In this paper, we study the thermodynamics of the Schwarzschild and the Reissner–Nordström black holes surrounded by quintessence. By using the thermodynamical laws of the black holes, we derive the thermodynamic properties of these black holes and we compare the results with each other. We investigate the mass, temperature and heat capacity as functions of entropy for these black holes. We also discuss the equation of state of the Schwarzschild and the Reissner–Nordström black holes surrounded by quintessence.

Effective Stringy Description of Schwarzschild Black Holes

OpenAIRE

Krasnov , Kirill; Solodukhin , Sergey N.

2004-01-01

We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background. For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified ``tortoise'' coordinate. The other Riemann surface appears when the radial wave equation is interpreted as the Fuchsian differential equation. We study these surfaces in detail for the BTZ and Schwarzschild black holes in four and higher dimensions....

The Planck Vacuum and the Schwarzschild Metrics

Directory of Open Access Journals (Sweden)

Daywitt W. C.

2009-07-01

Full Text Available The Planck vacuum (PV is assumed to be the source of the visible universe. So under conditions of sufficient stress, there must exist a pathway through which energy from the PV can travel into this universe. Conversely, the passage of energy from the visible universe to the PV must also exist under the same stressful conditions. The following examines two versions of the Schwarzschild metric equation for compatability with this open-pathway idea.

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

Energy Technology Data Exchange (ETDEWEB)

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

2013-04-01

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

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

International Nuclear Information System (INIS)

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

2013-01-01

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

Geodesic atlas-based labeling of anatomical trees

DEFF Research Database (Denmark)

Feragen, Aasa; Petersen, Jens; Owen, Megan

2015-01-01

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

Aplanatic telescopes based on Schwarzschild optical configuration: from grazing incidence Wolter-like x-ray optics to Cherenkov two-mirror normal incidence telescopes

Science.gov (United States)

Sironi, Giorgia

2017-09-01

At the beginning of XX century Karl Schwarzschild defined a method to design large-field aplanatic telescopes based on the use of two aspheric mirrors. The approach was then refined by Couder (1926) who, in order to correct for the astigmatic aberration, introduced a curvature of the focal plane. By the way, the realization of normal-incidence telescopes implementing the Schwarzschild aplanatic configuration has been historically limited by the lack of technological solutions to manufacture and test aspheric mirrors. On the other hand, the Schwarzschild solution was recovered for the realization of coma-free X-ray grazing incidence optics. Wolter-like grazing incidence systems are indeed free of spherical aberration, but still suffer from coma and higher order aberrations degrading the imaging capability for off-axis sources. The application of the Schwarzschild's solution to X-ray optics allowed Wolter to define an optical system that exactly obeys the Abbe sine condition, eliminating coma completely. Therefore these systems are named Wolter-Schwarzschild telescopes and have been used to implement wide-field X-ray telescopes like the ROSAT WFC and the SOHO X-ray telescope. Starting from this approach, a new class of X-ray optical system was proposed by Burrows, Burg and Giacconi assuming polynomials numerically optimized to get a flat field of view response and applied by Conconi to the wide field x-ray telescope (WFXT) design. The Schwarzschild-Couder solution has been recently re-discovered for the application to normal-incidence Cherenkov telescopes, thanks to the suggestion by Vassiliev and collaborators. The Italian Institute for Astrophysics (INAF) realized the first Cherenkov telescope based on the polynomial variation of the Schwarzschild configuration (the so-called ASTRI telescope). Its optical qualification was successfully completed in 2016, demonstrating the suitability of the Schwarzschild-like configuration for the Cherenkov astronomy requirements

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

Science.gov (United States)

Deng, Gao-Ming; Huang, Yong-Chang

2018-03-01

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

New mathematical framework for spherical gravitational collapse

International Nuclear Information System (INIS)

Giambo, Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo

2003-01-01

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non-static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates the existence of singular null geodesics to the existence of regular curves which are supersolutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed. (letter to the editor)

Entanglement redistribution in the Schwarzschild spacetime

International Nuclear Information System (INIS)

Wang, Jieci; Pan, Qiyuan; Jing, Jiliang

2010-01-01

The effect of Hawking radiation on the redistribution of the entanglement and mutual information in the Schwarzschild spacetime is investigated. Our analysis shows that the physically accessible correlations degrade while the unaccessible correlations increase as the Hawking temperature increases because the initial correlations described by inertial observers are redistributed between all the bipartite modes. It is interesting to note that, in the limit case that the temperature tends to infinity, the accessible mutual information equals to just half of its initial value, and the unaccessible mutual information between mode A and II also equals to the same value.

Karl Schwarzschild's investigations of `out-of-focus photometry' between 1897 and 1899 at Kuffner Observatory in Vienna

Science.gov (United States)

Habison, Peter

From 1897 to 1899 Karl Schwarzschild worked at the Kuffner Observatory in Vienna. During these years he developed new measuring techniques in the field of photographic photometry, where he studied particularly the quantitative determination of the departure from the reciprocity law during photographic exposure. This paper concentrates on Schwarzschild's early work in this field and gives an overview of his important Viennese years.

Uniqueness of the electrostatic solution in Schwarzschild space

International Nuclear Information System (INIS)

Molnar, Pal G.; Elsaesser, Klaus

2003-01-01

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof

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

Science.gov (United States)

Fröb, Markus B.

2018-02-01

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

Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion

Science.gov (United States)

Barack, Leor

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

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

International Nuclear Information System (INIS)

Erkal, Cahit

2006-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2006-07-01

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

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

Science.gov (United States)

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

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

On stellar collapse: continual or oscillatory. A short comment

International Nuclear Information System (INIS)

Leung, P.T.

1980-01-01

We comment on a previously published paper on the oscillatory dynamics of stellar collapse and conclude that the Schwarzschild interior solution applied to the 'inflection points' can never give rise to a 'turning back' motion, in spite of the fact that the geodesic equation really does not always describe an attractive gravitational acceleration

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

Science.gov (United States)

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

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

New perspectives for high accuracy SLR with second generation geodesic satellites

Science.gov (United States)

Lund, Glenn

1993-01-01

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

General relativity

International Nuclear Information System (INIS)

Gourgoulhon, Eric

2013-01-01

The author proposes a course on general relativity. He first presents a geometrical framework by addressing, presenting and discussion the following notions: the relativistic space-time, the metric tensor, Universe lines, observers, principle of equivalence and geodesics. In the next part, he addresses gravitational fields with spherical symmetry: presentation of the Schwarzschild metrics, radial light geodesics, gravitational spectral shift (Einstein effect), orbitals of material objects, photon trajectories. The next parts address the Einstein equation, black holes, gravitational waves, and cosmological solutions. Appendices propose a discussion of the relationship between relativity and GPS, some problems and their solutions, and Sage codes

Schwarzschild black holes can wear scalar wigs.

Science.gov (United States)

Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Núñez, Darío; Sarbach, Olivier

2012-08-24

We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.

Geodesic least squares regression for scaling studies in magnetic confinement fusion

International Nuclear Information System (INIS)

Verdoolaege, Geert

2015-01-01

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

Ergodic Properties of the Quantum Geodesic Flow on Tori

Energy Technology Data Exchange (ETDEWEB)

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

2005-05-15

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

FRW cosmological model inside an isolated Schwarzschild black hole

OpenAIRE

Ortiz, C.; Rosales, J. J.; Socorro, J.; Tkach, V. I.

2004-01-01

Using the canonical quantum theory of spherically symmetric pure gravitational systems, we present a direct correspondence between the Friedmann-Robertson-Walker (FRW) cosmological model in the interior of a Schwarzschild black hole and the nth energy eigenstate of a linear harmonic oscillator. Such type of universe has a quantized mass of the order of the Planck mass and harmonic oscillator wave functions

Minimal conditions for the existence of a Hawking-like flux

International Nuclear Information System (INIS)

Barcelo, Carlos; Liberati, Stefano; Sonego, Sebastiano; Visser, Matt

2011-01-01

We investigate the minimal conditions that an asymptotically flat general relativistic spacetime must satisfy in order for a Hawking-like Planckian flux of particles to arrive at future null infinity. We demonstrate that there is no requirement that any sort of horizon form anywhere in the spacetime. We find that the irreducible core requirement is encoded in an approximately exponential 'peeling' relationship between affine coordinates on past and future null infinity. As long as a suitable adiabaticity condition holds, then a Planck-distributed Hawking-like flux will arrive at future null infinity with temperature determined by the e-folding properties of the outgoing null geodesics. The temperature of the Hawking-like flux can slowly evolve as a function of time. We also show that the notion of peeling of null geodesics is distinct from the usual notion of 'inaffinity' used in Hawking's definition of surface gravity.

Thermodynamic stability of modified Schwarzschild-AdS black hole in rainbow gravity

Energy Technology Data Exchange (ETDEWEB)

Kim, Yong-Wan [Chonbuk National University, Research Institute of Physics and Chemistry, Jeonju (Korea, Republic of); Kim, Seung Kook [Seonam University, Department of Physical Therapy, Namwon (Korea, Republic of); Park, Young-Jai [Sogang University, Department of Physics, Seoul (Korea, Republic of)

2016-10-15

In this paper, we have extended the previous study of the thermodynamics and phase transition of the Schwarzschild black hole in the rainbow gravity to the Schwarzschild-AdS black hole where metric depends on the energy of a probe. Making use of the Heisenberg uncertainty principle and the modified dispersion relation, we have obtained the modified local Hawking temperature and thermodynamic quantities in an isothermal cavity. Moreover, we carry out the analysis of constant temperature slices of a black hole. As a result, we have shown that there also exists another Hawking-Page-like phase transition in which case a locally stable small black hole tunnels into a globally stable large black hole as well as the standard Hawking-Page phase transition from a hot flat space to a black hole. (orig.)

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

International Nuclear Information System (INIS)

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

2016-01-01

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

(Anti-)Evaporation of Schwarzschild-de Sitter Black Holes

OpenAIRE

Bousso, Raphael; Hawking, Stephen

1997-01-01

We study the quantum evolution of black holes immersed in a de Sitter background space. For black holes whose size is comparable to that of the cosmological horizon, this process differs significantly from the evaporation of asymptotically flat black holes. Our model includes the one-loop effective action in the s-wave and large N approximation. Black holes of the maximal mass are in equilibrium. Unexpectedly, we find that nearly maximal quantum Schwarzschild-de Sitter black holes anti-evapor...

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

International Nuclear Information System (INIS)

Nolan, Brien C; Debnath, Ujjal

2007-01-01

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

Investigation of energetic particle induced geodesic acoustic mode

Science.gov (United States)

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

2017-10-01

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

Linearized stability analysis of thin-shell wormholes with a cosmological constant

International Nuclear Information System (INIS)

Lobo, Francisco S N; Crawford, Paulo

2004-01-01

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a 0 ≤ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius

The 100th birthday of the conic constant and Schwarzschild's revolutionary papers in optics

Science.gov (United States)

Rakich, Andrew

2005-08-01

In 1905 Karl Schwarzschild published three papers on optics, two of which revolutionized the field of reflecting telescope optics. In his first paper he developed a full theory of the aberrations of reflecting telescopes, generalizing the Eikonal of Bruns to take into account systems with an infinite long conjugate. In the second paper Schwarzschild applied his formulation to a masterful analysis of 2 mirror anastigmatic systems, along the way discovering the so called Ritchey-Chretien aplanat, 18 years Ritchey and Chretien's announcement. Numerous other innovations are given in what must be seen as being among the most important papers on the aberrations of optical systems ever written.

Neutrino fields in Einstein-Cartan theory

International Nuclear Information System (INIS)

Griffiths, J.B.

1981-01-01

The spin-coefficient formalism presented elsewhere is here applied to classical neutrino fields in Einstein-Cartan theory. It is shown that the neutrino current vector is tangent to an expansion-free null geodesic congruence with constant and equal twist and shear, which vanish if and only if the congruence is a repeated principal null congruence of the gravitational field. The geodesics are both extremals and autoparallels. All exact solutions for the case of pure radiation fields are obtained, and it is shown that the only possible ghost solutions have a plane wave metric. (author)

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

Science.gov (United States)

Kuznetsov, Sergey P.

2016-12-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-01-24

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

Event horizon and scalar potential

International Nuclear Information System (INIS)

Duruisseau, J.P.; Tonnelat, M.A.

1977-01-01

The introduction of a scalar potential with a more general scheme than General Relativity eliminates the event horizon. Among possible solutions, the Schwarzschild one represents a singular case. A study of the geodesic properties of the matching with an approximated interior solution are given. A new definition of the gravitational mass and chi function is deduced. (author)

Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity

International Nuclear Information System (INIS)

Bernuzzi, Sebastiano; Nagar, Alessandro; Zenginoglu, Anil

2011-01-01

We compute and analyze the gravitational waveform emitted to future null infinity by a system of two black holes in the large-mass-ratio limit. We consider the transition from the quasiadiabatic inspiral to plunge, merger, and ringdown. The relative dynamics is driven by a leading order in the mass ratio, 5PN-resummed, effective-one-body (EOB), analytic-radiation reaction. To compute the waveforms, we solve the Regge-Wheeler-Zerilli equations in the time-domain on a spacelike foliation, which coincides with the standard Schwarzschild foliation in the region including the motion of the small black hole, and is globally hyperboloidal, allowing us to include future null infinity in the computational domain by compactification. This method is called the hyperboloidal layer method, and is discussed here for the first time in a study of the gravitational radiation emitted by black hole binaries. We consider binaries characterized by five mass ratios, ν=10 -2,-3,-4,-5,-6 , that are primary targets of space-based or third-generation gravitational wave detectors. We show significative phase differences between finite-radius and null-infinity waveforms. We test, in our context, the reliability of the extrapolation procedure routinely applied to numerical relativity waveforms. We present an updated calculation of the final and maximum gravitational recoil imparted to the merger remnant by the gravitational wave emission, v kick end /(cν 2 )=0.04474±0.00007 and v kick max /(cν 2 )=0.05248±0.00008. As a self-consistency test of the method, we show an excellent fractional agreement (even during the plunge) between the 5PN EOB-resummed mechanical angular momentum loss and the gravitational wave angular momentum flux computed at null infinity. New results concerning the radiation emitted from unstable circular orbits are also presented. The high accuracy waveforms computed here could be considered for the construction of template banks or for calibrating analytic models such

Covariant perturbations of Schwarzschild black holes

International Nuclear Information System (INIS)

Clarkson, Chris A; Barrett, Richard K

2003-01-01

We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black-hole spacetime. The 1 + 3 covariant approach is extended to a '1 + 1 + 2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this. The background Schwarzschild solution is discussed and a covariant characterization is given. We give the full first-order system of linearized 1 + 1 + 2 covariant equations, and we show how, by introducing (time and spherical) harmonic functions, these may be reduced to a system of first-order ordinary differential equations and algebraic constraints for the 1 + 1 + 2 variables which may be solved straightforwardly. We show how both odd- and even-parity perturbations may be unified by the discovery of a covariant, frame- and gauge-invariant, transverse-traceless tensor describing gravitational waves, which satisfies a covariant wave equation equivalent to the Regge-Wheeler equation for both even- and odd-parity perturbations. We show how the Zerilli equation may be derived from this tensor, and derive a similar transverse-traceless tensor equation equivalent to this equation. The so-called special quasinormal modes with purely imaginary frequency emerge naturally. The significance of the degrees of freedom in the choice of the two frame vectors is discussed, and we demonstrate that, for a certain frame choice, the underlying dynamics is governed purely by the Regge-Wheeler tensor. The two transverse-traceless Weyl tensors which carry the curvature of gravitational waves are discussed, and we give the closed system of four first-order ordinary differential equations describing their propagation. Finally, we consider the extension of this work to the study of

Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity

Energy Technology Data Exchange (ETDEWEB)

Sibandze, Dan B.; Goswami, Rituparno; Maharaj, Sunil D.; Nzioki, Anne Marie [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, Private Bag X54001, Durban (South Africa); Dunsby, Peter K.S. [University of Cape Town, Department of Mathematics and Applied Mathematics and ACGC, Cape Town (South Africa)

2017-06-15

It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures of the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this paper we consider the perturbations of Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equation that governs these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. (orig.)

The topology of geodesically complete space-times

International Nuclear Information System (INIS)

Lee, C.W.

1983-01-01

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

Perfect fluid models in noncomoving observational spherical coordinates

International Nuclear Information System (INIS)

Ishak, Mustapha

2004-01-01

We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null geodesic equation is not integrable in general. Our choice of null coordinates solves the radial ingoing null geodesic by construction. Furthermore, we use an approach where the velocity field is uniquely calculated from the metric rather than put in by hand. Conveniently, this allows us to explore models in a noncomoving frame of reference. In this frame, we find that the velocity field has shear, acceleration, and expansion rate in general. We show that a comoving frame is not compatible with expanding perfect fluid models in the coordinates proposed and dust models are simply not possible. We describe the models in a noncomoving frame. We use the dust models in a noncomoving frame to outline a fitting procedure

On scattering of scalar waves in static space-times, particularly Schwarzschild

International Nuclear Information System (INIS)

Beig, R.

1982-01-01

This paper aims at laying foundations of a rigorous scattering theory for scalar waves in a static space-time. The treatment includes geometries which can be thought of as representing the exterior of a black hole. Schwarzschild space-time, as a particular example, is studied in more detail. (Auth.)

A Finsler geodesic spray paradigm for wildfire spread modelling

DEFF Research Database (Denmark)

Markvorsen, Steen

2015-01-01

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

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

Science.gov (United States)

Thornburg, Jonathan

2007-01-01

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well

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

Science.gov (United States)

Jacobson, Daniel; Stratt, Richard M.

2014-05-01

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

An exact Jacobi map in the geodesic light-cone gauge

CERN Document Server

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

2013-11-07

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

Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

Science.gov (United States)

Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang

2017-11-01

We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

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

International Nuclear Information System (INIS)

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

1981-01-01

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

Hawking radiation inside a Schwarzschild black hole

Science.gov (United States)

Hamilton, Andrew J. S.

2018-05-01

The boundary of any observer's spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer's spacetime in the presence of a black hole is not the true (future event) horizon of the black hole, but rather the illusory horizon, the dimming, redshifting surface of the star that collapsed to the black hole long ago. The illusory horizon is the source of Hawking radiation seen by observers both outside and inside the true horizon. The perceived acceleration (gravity) on the illusory horizon sets the characteristic frequency scale of Hawking radiation, even if that acceleration varies dynamically, as it must do from the perspective of an infalling observer. The acceleration seen by a non-rotating free-faller both on the illusory horizon below and in the sky above is calculated for a Schwarzschild black hole. Remarkably, as an infaller approaches the singularity, the acceleration becomes isotropic, and diverging as a power law. The isotropic, power-law character of the Hawking radiation, coupled with conservation of energy-momentum, the trace anomaly, and the familiar behavior of Hawking radiation far from the black hole, leads to a complete description of the quantum energy-momentum inside a Schwarzschild black hole. The quantum energy-momentum near the singularity diverges as r^{-6}, and consists of relativistic Hawking radiation and negative energy vacuum in the ratio 3 : - 2. The classical back reaction of the quantum energy-momentum on the geometry, calculated using the Einstein equations, serves merely to exacerbate the singularity. All the results are consistent with traditional calculations of the quantum energy-momentum in 1 + 1 spacetime dimensions.

New non-linear modified massless Klein-Gordon equation

Energy Technology Data Exchange (ETDEWEB)

Asenjo, Felipe A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Facultad de Ingenieria y Ciencias, Santiago (Chile); Hojman, Sergio A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Santiago (Chile); Universidad de Chile, Departamento de Fisica, Facultad de Ciencias, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2017-11-15

The massless Klein-Gordon equation on arbitrary curved backgrounds allows for solutions which develop ''tails'' inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless Klein-Gordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current-current interaction. Its non-linearity is due to a self-coupling term which is related to the quantum mechanical Bohm potential. (orig.)

Arcmancer: Geodesics and polarized radiative transfer library

Science.gov (United States)

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

2018-05-01

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

Interactive Visualization of a Thin Disc around a Schwarzschild Black Hole

Science.gov (United States)

Muller, Thomas; Frauendiener, Jorg

2012-01-01

In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a…

Regular coordinate systems for Schwarzschild and other spherical spacetimes

OpenAIRE

Martel, Karl; Poisson, Eric

2000-01-01

The continuation of the Schwarzschild metric across the event horizon is almost always (in textbooks) carried out using the Kruskal-Szekeres coordinates, in terms of which the areal radius r is defined only implicitly. We argue that from a pedagogical point of view, using these coordinates comes with several drawbacks, and we advocate the use of simpler, but equally effective, coordinate systems. One such system, introduced by Painleve and Gullstrand in the 1920's, is especially simple and pe...

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

International Nuclear Information System (INIS)

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

2014-01-01

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

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

International Nuclear Information System (INIS)

Yehia, Hamad M

2013-01-01

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

Average geodesic distance of skeleton networks of Sierpinski tetrahedron

Science.gov (United States)

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

2018-04-01

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

Statistical metastability of a classical ideal gas in the Schwarzschild gravitational field

International Nuclear Information System (INIS)

Gaina, A.B.; Zaslavskii, O.B.

1990-01-01

A classical ideal gas in the Schwarzschild gravitational field is considered. The lifetime of a gas influenced by thermal fluctuations has been calculated. It is shown that thermal effects can lead to the electric charging of a black hole in a plasma containing particles with different masses. (author)

Geodesic acoustic modes in noncircular cross section tokamaks

Energy Technology Data Exchange (ETDEWEB)

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

2017-03-15

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

Fundamental geodesic deformations in spaces of treelike shapes

DEFF Research Database (Denmark)

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

2010-01-01

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

An absence theorem for static wave maps in the Schwarzschild-AdS spacetime

International Nuclear Information System (INIS)

Xie Naqing

2005-01-01

In this Letter, we obtain an absence theorem for static wave maps defined from the Schwarzschild-anti de Sitter spacetime into any Riemannian manifold. This work extends the results in [Chinese Ann. Math. B 5 (1984) 737, Lett. Math. Phys. 14 (1987) 343

A Continuum Mechanical Approach to Geodesics in Shape Space

Science.gov (United States)

2010-01-01

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

QFT holography near the horizon of Schwarzschild-like spacetimes

OpenAIRE

Moretti, Valter; Pinamonti, Nicola

2003-01-01

It is argued that free QFT can be defined on the event horizon of a Schwarzschild-like spacetime and that this theory is unitarily and algebraically equivalent to QFT in the bulk (near the horizon). Under that unitary equivalence the bulk hidden SL(2,R) symmetry found in a previous work becomes manifest on the event horizon, it being induced by a group of horizon diffeomorphisms. The class of generators of that group can be enlarged to include a full Virasoro algebra of fields which are defin...

Event and Apparent Horizon Finders for 3+1 Numerical Relativity

Directory of Open Access Journals (Sweden)

Thornburg Jonathan

2007-06-01

Full Text Available Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3+1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous null surface in spacetime. The event horizon is defined nonlocally in time: it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part of spacetime has been numerically computed.There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate.In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Theta. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most “apparent horizon” finders actually find MOTSs.There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting

Wormholes supported by phantom energy from Shan-Chen cosmological fluids

Energy Technology Data Exchange (ETDEWEB)

Wang, Deng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Meng, Xin-He [Nankai University, Department of Physics, Tianjin (China); Institute of Theoretical Physics, CAS, State key Lab of Theoretical Physics, Beijing (China)

2016-03-15

In the present paper, the exact solutions of spherically symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan-Chen background fluid are obtained. We have considered the important case of the model parameter ψ ∼ 1, which corresponds to the ''saturation effect'', and this regime corresponds to an effective form of ''asymptotic freedom'' for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range for the values of the model parameters g and ω when the spacetime metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Furthermore, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and analyze the traversabilities of the wormholes. Finally, we consider the case of anisotropic pressure and discover that the transverse pressure also crosses the phantom divide -1 with the growth of the wormhole dimension, and it tends to be the same as the radial pressure with the growth of the wormhole radius. (orig.)

Null-strut calculus. II. Dynamics

International Nuclear Information System (INIS)

Kheyfets, A.; LaFave, N.J.; Miller, W.A.

1990-01-01

In this paper, we continue from the preceding paper to develop a fully functional Regge calculus geometrodynamic algorithm from the null-strut-calculus construction. The developments discussed include (a) the identification of the Regge calculus analogue of the constraint and evolution equations on the null-strut lattice, (b) a description of the Minkowski solid geometry for the simplicial blocks of the null-strut lattice, (c) a description of the evolution algorithm for the geometrodynamic scheme and an analysis of its consistency, and (d) a presentation of the dynamical degrees of freedom for a simplicial hypersurface and the description of an initial-value prescription. To demonstrate qualitatively this new approach to geometrodynamics, we present the most simple application of null-strut calculus that we know of---the Friedmann cosmology using the three-boundary of a 600-cell simplicial polytope to model the simplicial hypersurface

Visible Nulling Coronagraph Progress Report

Science.gov (United States)

Lyon, R. G.; Clampin, M.; Woodruff, R. A.; Vasudevan, G.; Thompson, P.; Petrone, P.; Madison, T.; Rizzo, M.; Melnick, G.; Tolls, V.

2010-10-01

We report on recent laboratory results with the NASA Goddard Space Flight Center Visible Nulling Coronagraph (VNC) testbed. We have achieved focal plane contrasts of 108 and approaching 109 at inner working angles of 2 λ/D and 4 λ/D, respectively. Results were obtained with a broadband source and 40 nm filter centered on 630 nm. A null control breadboard (NCB) was also developed to assess and quantify MEMS based deformable mirror technology (DM), and to develop and assess closed-loop null control algorithms. We have demonstrated closed-loop performance at 27 Hz.

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

International Nuclear Information System (INIS)

Liu Hongya

1987-01-01

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

On electric field in anti-de Sitter spacetime

Energy Technology Data Exchange (ETDEWEB)

Cheong, Lee Yen, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Yan, Chew Xiao, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Ching, Dennis Ling Chuan, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my [Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Bandar Seri Iskandar, Tronoh 31750, Perak (Malaysia)

2014-10-24

In this paper we calculate the electromagnetic field produced using retarded Green's function in Anti-de Sitter spacetime (AdS). Since this spacetime is non-globally hyperbolic and has no Cauchy surface, we only consider the field originated from a charge moving along its geodesic in the region consists of points covered by future null geodesic of the charge.

Astronomy from Olbers to Schwarzschild. (German Title: Astronomie von Olbers bis Schwarzschild)

Science.gov (United States)

Dick, Wolfgang R.; Hamel, Jürgen

This issue comprises talks presented 2000 September 18 at the colloquium ``International relations in astronomy'' it is supplemented by additional articles about this topic. The foundation of the international ``Vereinigte Astronomische Gesellschaft'', which took place in 1800 in Bremen, prompted us to investigate the development of astronomy in German-speaking regions, and its international relations during the 19th century. We investigate the activities of famous astronomers like W. Olbers, J.E. Bode, F.X. von Zach, J.H. Schroeter, H.C. Schumacher and K. Schwarzschild, as well as those of their less famous professional colleagues like J.G. Schrader and L. de Ball. The geographical spectrum extends from Bremen and Lilienthal over Kiel, Gotha and Dresden to Copenhagen, Vienna and Chile. Among the topics are: telescope construction, including telescopes made by Herschel, the rediscovery of the minor planet Ceres 1801/02, the Berlin ``Astronomisches Jahrbuch'', the foundation of the ``Astronomische Nachrichten'', the evolution from the ``Vereinigte Astronomische Gesellschaft'' to the present-day ``Astronomische Gesellschaft'', the research at the Kuffner Observatory in Vienna, the professionalization in astronomy, and the attempts of many countries to establish a southern observatory in Chile. A listing of astronomical monuments in Lilienthal and Bremen concludes the book. All papers are written in German with English abstracts.

Anatomy of geodesic Witten diagrams

Energy Technology Data Exchange (ETDEWEB)

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

2017-05-12

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

Can one increase the luminosity of a Schwarzschild black hole?

OpenAIRE

Mayo, Avraham E.

2000-01-01

We illustrate how Hawking's radiance from a Schwarzschild black hole is modified by the electrostatic self-interaction of the emitted charged particles. A W.K.B approximation shows that the probability for a self-interacting charged particle to propagate from the interior to the exterior of the horizon is increased relative to the corresponding probability for neutral particles. We also demonstrate how the electric potential of a charged test object in the black hole's vicinity gives rise to ...

Visible nulling coronagraph testbed results

Science.gov (United States)

Lyon, Richard G.; Clampin, Mark; Woodruff, Robert A.; Vasudevan, Gopal; Thompson, Patrick; Petrone, Peter; Madison, Timothy; Rizzo, Maxime; Melnick, Gary; Tolls, Volker

2009-08-01

We report on our recent laboratory results with the NASA/Goddard Space Flight Center (GSFC) Visible Nulling Coronagraph (VNC) testbed. We have experimentally achieved focal plane contrasts of 1 x 108 and approaching 109 at inner working angles of 2 * wavelength/D and 4 * wavelength/D respectively where D is the aperture diameter. The result was obtained using a broadband source with a narrowband spectral filter of width 10 nm centered on 630 nm. To date this is the deepest nulling result with a visible nulling coronagraph yet obtained. Developed also is a Null Control Breadboard (NCB) to assess and quantify MEMS based segmented deformable mirror technology and develop and assess closed-loop null sensing and control algorithm performance from both the pupil and focal planes. We have demonstrated closed-loop control at 27 Hz in the laboratory environment. Efforts are underway to first bring the contrast to > 109 necessary for the direct detection and characterization of jovian (Jupiter-like) and then to > 1010 necessary for terrestrial (Earth-like) exosolar planets. Short term advancements are expected to both broaden the spectral passband from 10 nm to 100 nm and to increase both the long-term stability to > 2 hours and the extent of the null out to a ~ 10 * wavelength / D via the use of MEMS based segmented deformable mirror technology, a coherent fiber bundle, achromatic phase shifters, all in a vacuum chamber at the GSFC VNC facility. Additionally an extreme stability textbook sized compact VNC is under development.

Canonical quantization inside the Schwarzschild black hole

Science.gov (United States)

Yajnik, U. A.; Narayan, K.

1998-05-01

We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition. For the interior we appeal to CPT invariance to construct an explicitly positive-definite operator which allows identification of positive and negative frequencies. This operator is the translation operator corresponding to the inexorable propagation to smaller radii as expected from the classical metric. We also propose an expression for the propagator in the interior and express it as a mode sum. The field theory thus obtained is meaningful for small curvatures far from the classical singularity.

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

International Nuclear Information System (INIS)

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

1980-01-01

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

Null structure groups in eleven dimensions

International Nuclear Information System (INIS)

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

2006-01-01

We classify all the structure groups which arise as subgroups of the isotropy group (Spin(7)xR 8 )xR, of a single null Killing spinor in 11 dimensions. We construct the spaces of spinors fixed by these groups. We determine the conditions under which structure subgroups of the maximal null structure group (Spin(7)xR 8 )xR may also be embedded in SU(5), and hence the conditions under which a supersymmetric spacetime admits only null, or both timelike and null, Killing spinors. We discuss how this purely algebraic material will facilitate the direct analysis of the Killing spinor equation of 11 dimensional supergravity, and the classification of supersymmetric spacetimes therein

Perturbative calculation of quasinormal modes of AdS Schwarzschild black holes

International Nuclear Information System (INIS)

Musiri, Suphot; Ness, Scott; Siopsis, George

2006-01-01

We calculate analytically quasinormal modes of AdS Schwarzschild black holes including first-order corrections. We consider massive scalar, gravitational and electromagnetic perturbations. Our results are in good agreement with numerical calculations. In the case of electromagnetic perturbations, ours is the first calculation to provide an analytic expression for quasinormal frequencies, because the effective potential vanishes at zeroth order. We show that the first-order correction is logarithmic

Thermal properties of Green's functions in Rindler, de Sitter, and Schwarzschild spaces

International Nuclear Information System (INIS)

Dowker, J.S.

1978-01-01

The conventional massless scalar Green's functions in the Minkowski, de Sitter, and two-dimensional Schwarzschild spaces are reinterpreted as finite-temperature Green's functions and the corresponding averages of the stress-energy operator are calculated. The renormalization adopted consists of subtracting the zero-temperature quantities. In all cases the averages give the stress tensor of a purely Planck-type perfect gas

Nonexistence theorems for Yang-Mills fields and harmonic maps in the Schwarzschild spacetime

International Nuclear Information System (INIS)

Hu Hesheng

1987-01-01

The nonexistence of static solutions to pure Yang-Mills equations and nonconstant harmonic maps defined on the Schwarzschild spacetime outside the black hole (r>2M) is considered. Nonexistence theorems for pure Yang-Mills equations and harmonic maps in the region r≥5M and r≥3M are obtained, respectively. (orig.)

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

Science.gov (United States)

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

2010-08-01

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

Numerical calculations near spatial infinity

International Nuclear Information System (INIS)

Zenginoglu, Anil

2007-01-01

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

Two fluid plasmas in the vicinity of a Schwarzschild black hole

International Nuclear Information System (INIS)

Buzzi, V.; Hines, K.C.

1992-01-01

The 3+1 split of general relativity has been used to investigate the dispersion relation for certain plasma waves, together with the two stream instability, in the vicinity of a Schwarzschild black hole horizon. In contrast to the special relativistic results, the dispersion relations discussed here contain additional terms involving the gravitational acceleration, a, and the lapse function α. Some of these terms are imaginary and should correspond to gravitational damping effects. 5 refs

Drude-Schwarzschild Metric and the Electrical Conductivity of Metals

Directory of Open Access Journals (Sweden)

Silva P. R.

2014-07-01

Full Text Available Starting from a string with a length equal to the electron mean free path and having a unit cell equal to the Compton length of the electron, we construct a Schwarzschild-like metric. We found that this metric has a surface horizon with radius equal to the electron mean free path and its Bekenstein-like entropy is proportional to the number of squared unit cells contained in this spherical surface. The Hawking temperature is inversely proportional to the perimeter of the maximum circle of this sphere. Also, interesting analogies on some features of the particle physics are examined.

Accretion onto a noncommutative-inspired Schwarzschild black hole

Science.gov (United States)

Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna

2018-05-01

In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.

On the null origin of the ambitwistor string

Energy Technology Data Exchange (ETDEWEB)

Casali, Eduardo [Mathematical Institute, University of Oxford,Woodstock Road, Oxford, OX2 6GG (United Kingdom); Tourkine, Piotr [Department of Applied Mathematics and Theoretical Physics,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)

2016-11-07

In this paper we present the null string origin of the ambitwistor string. Classically, the null string is the tensionless limit of string theory, and so too is the ambitwistor string. Both have as constraint algebra the Galilean Conformal Algebra in two dimensions. But something interesting happens in the quantum theory since there is an ambiguity in quantizing the null string. We show that, given a particular choice of quantization scheme and a particular gauge, the null string coincides with the ambitwistor string both classically and quantum mechanically. We also show that the same holds for the spinning versions of the null string and ambitwistor string. With these results we clarify the relationship between the ambitwistor string, the null string, the usual string and the Hohm-Siegel-Zwiebach theory.

Exact Mathisson-Papapetrou equations in the Schwarzschild metric with integrals of motion

International Nuclear Information System (INIS)

Plyatsko, R.M.; Stefanishin, O.B.

2011-01-01

A new representation for exact Mathisson-Papapetrou equations under the Mathisson-Pirani condition in the Schwarzschild gravitational field, which does not contain third-order derivatives with respect to spinning particle coordinates, has been obtained. For this purpose, the integrals of energy and angular momentum of a spinning particle, as well as a differential relation following from the Mathisson-Papapetrou equations for an arbitrary metric, are used.

[Dilemma of null hypothesis in ecological hypothesis's experiment test.

Science.gov (United States)

Li, Ji

2016-06-01

Experimental test is one of the major test methods of ecological hypothesis, though there are many arguments due to null hypothesis. Quinn and Dunham (1983) analyzed the hypothesis deduction model from Platt (1964) and thus stated that there is no null hypothesis in ecology that can be strictly tested by experiments. Fisher's falsificationism and Neyman-Pearson (N-P)'s non-decisivity inhibit statistical null hypothesis from being strictly tested. Moreover, since the null hypothesis H 0 (α=1, β=0) and alternative hypothesis H 1 '(α'=1, β'=0) in ecological progresses are diffe-rent from classic physics, the ecological null hypothesis can neither be strictly tested experimentally. These dilemmas of null hypothesis could be relieved via the reduction of P value, careful selection of null hypothesis, non-centralization of non-null hypothesis, and two-tailed test. However, the statistical null hypothesis significance testing (NHST) should not to be equivalent to the causality logistical test in ecological hypothesis. Hence, the findings and conclusions about methodological studies and experimental tests based on NHST are not always logically reliable.

Gravitational collapse of a cylindrical null shell in vacuum

Directory of Open Access Journals (Sweden)

S. Khakshournia

2008-03-01

Full Text Available   Barrabès-Israel null shell formalism is used to study the gravitational collapse of a thin cylindrical null shell in vacuum. In general the lightlike matter shell whose history coincides with a null hypersurface is characterized by a surface energy density. In addition, a gravitational impulsive wave is present on this null hypersurface whose generators admit both the shear and expansion. In the case of imposing the cylindrical flatness the surface energy-momentum tensor of the matter shell on the null hypersurface vanishes and the null hyper- surface is just the history of the gravitational wave .

The Event Horizon of The Schwarzschild Black Hole in Noncommutative Spaces

OpenAIRE

Nasseri, Forough

2005-01-01

The event horizon of Schwarzschild black hole is obtained in noncommutative spaces up to the second order of perturbative calculations. Because this type of black hole is non-rotating, to the first order there is no any effect on the event horizon due to the noncommutativity of space. A lower limit for the noncommutativity parameter is also obtained. As a result, the event horizon in noncommutative spaces is less than the event horizon in commutative spaces.

Quasinormal modes of the near extremal Schwarzschild-de Sitter black hole

International Nuclear Information System (INIS)

Cardoso, Vitor; Lemos, Jose P.S.

2003-01-01

We present an exact expression for the quasinormal modes of scalar, electromagnetic, and gravitational perturbations of a near extremal Schwarzschild-de Sitter black hole and we show that is why a previous approximation holds exactly in this near extremal regime. In particular, our results give the asymptotic behavior of the quasinormal frequencies for highly damped modes, which has recently attracted much attention due to the proposed identification of its real part with the Barbero-Immirzi parameter

Bare Quantum Null Energy Condition.

Science.gov (United States)

Fu, Zicao; Marolf, Donald

2018-02-16

The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC is intrinsically finite. We study the more general case here where they do not and argue that a QNEC can still hold for bare (unrenormalized) quantities. While the original QNEC applied only to locally stationary null congruences in backgrounds that solve semiclassical theories of quantum gravity, at least in the formal perturbation theory at a small Planck length, the quantum focusing conjecture can be viewed as the special case of our bare QNEC for which the metric is on shell.

Supersymmetric null-like holographic cosmologies

International Nuclear Information System (INIS)

Lin Fengli; Wen Wenyu

2006-01-01

We construct a new class of 1/4-BPS time dependent domain-wall solutions with null-like metric and dilaton in type II supergravities, which admit a null-like big bang singularity. Based on the domain-wall/QFT correspondence, these solutions are dual to 1/4-supersymmetric quantum field theories living on a boundary cosmological background with time dependent coupling constant and UV cutoff. In particular we evaluate the holographic c function for the 2-dimensional dual field theory living on the corresponding null-like cosmology. We find that this c function runs in accordance with the c-theorem as the boundary universe evolves, this means that the number of degrees of freedom is divergent at big bang and suggests the possible resolution of big bang singularity

Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle

Energy Technology Data Exchange (ETDEWEB)

Feng, Z.W.; Zu, X.T. [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Li, H.L. [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); Yang, S.Z. [China West Normal University, Physics and Space Science College, Nanchong (China)

2016-04-15

We investigate the thermodynamics of Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle (GUP). The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of the Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of the black hole approaches the order of Planck scale, it stops radiating and leads to a black hole remnant. Meanwhile, the Planck scale remnant can be confirmed through the analysis of the heat capacity. Those phenomena imply that the GUP may give a way to solve the information paradox. Besides, we also investigate the possibilities to observe the black hole at the Large Hadron Collider (LHC), and the results demonstrate that the black hole cannot be produced in the recent LHC. (orig.)

MAGNETIC NULL POINTS IN KINETIC SIMULATIONS OF SPACE PLASMAS

International Nuclear Information System (INIS)

Olshevsky, Vyacheslav; Innocenti, Maria Elena; Cazzola, Emanuele; Lapenta, Giovanni; Deca, Jan; Divin, Andrey; Peng, Ivy Bo; Markidis, Stefano

2016-01-01

We present a systematic attempt to study magnetic null points and the associated magnetic energy conversion in kinetic particle-in-cell simulations of various plasma configurations. We address three-dimensional simulations performed with the semi-implicit kinetic electromagnetic code iPic3D in different setups: variations of a Harris current sheet, dipolar and quadrupolar magnetospheres interacting with the solar wind, and a relaxing turbulent configuration with multiple null points. Spiral nulls are more likely created in space plasmas: in all our simulations except lunar magnetic anomaly (LMA) and quadrupolar mini-magnetosphere the number of spiral nulls prevails over the number of radial nulls by a factor of 3–9. We show that often magnetic nulls do not indicate the regions of intensive energy dissipation. Energy dissipation events caused by topological bifurcations at radial nulls are rather rare and short-lived. The so-called X-lines formed by the radial nulls in the Harris current sheet and LMA simulations are rather stable and do not exhibit any energy dissipation. Energy dissipation is more powerful in the vicinity of spiral nulls enclosed by magnetic flux ropes with strong currents at their axes (their cross sections resemble 2D magnetic islands). These null lines reminiscent of Z-pinches efficiently dissipate magnetic energy due to secondary instabilities such as the two-stream or kinking instability, accompanied by changes in magnetic topology. Current enhancements accompanied by spiral nulls may signal magnetic energy conversion sites in the observational data

The Compton-Schwarzschild correspondence from extended de Broglie relations

Energy Technology Data Exchange (ETDEWEB)

Lake, Matthew J. [The Institute for Fundamental Study, “The Tah Poe Academia Institute' ,Naresuan University, Phitsanulok 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education,Bangkok 10400 (Thailand); Carr, Bernard [School of Physics and Astronomy, Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)

2015-11-17

The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial gravity. In a mass-radius diagram, the two lines intersect near the Planck point (l{sub P},m{sub P}), where quantum gravity effects become significant. Since canonical (non-gravitational) quantum mechanics is based on the concept of wave-particle duality, encapsulated in the de Broglie relations, these relations should break down near (l{sub P},m{sub P}). It is unclear what physical interpretation can be given to quantum particles with energy E≫m{sub P}c{sup 2}, since they correspond to wavelengths λ≪l{sub P} or time periods τ≪t{sub P} in the standard theory. We therefore propose a correction to the standard de Broglie relations, which gives rise to a modified Schrödinger equation and a modified expression for the Compton wavelength, which may be extended into the region E≫m{sub P}c{sup 2}. For the proposed modification, we recover the expression for the Schwarzschild radius for E≫m{sub P}c{sup 2} and the usual Compton formula for E≪m{sub P}c{sup 2}. The sign of the inequality obtained from the uncertainty principle reverses at m≈m{sub P}, so that the Compton wavelength and event horizon size may be interpreted as minimum and maximum radii, respectively. We interpret the additional terms in the modified de Broglie relations as representing the self-gravitation of the wave packet.

Divided Spheres Geodesics and the Orderly Subdivision of the Sphere

CERN Document Server

Popko, Edward S

2012-01-01

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

Geodesic Monitoring of Settling in Vertical Fuel Tanks

Directory of Open Access Journals (Sweden)

Luis Enrique Acosta-González

2017-07-01

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

Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk

Energy Technology Data Exchange (ETDEWEB)

Čížek, P.; Semerák, O., E-mail: oldrich.semerak@mff.cuni.cz [Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, Prague (Czech Republic)

2017-09-01

Will, in 1974, treated the perturbation of a Schwarzschild black hole due to a slowly rotating, light, concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to perturbation by a thin disk (which is more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they can be integrated out over the source (a thin disk in our case) to yield good converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disk, including the physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust in a circular orbit about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, as it is just carried along by the dragging effect of the disk.

Gravitational lens produces an odd number of images

International Nuclear Information System (INIS)

McKenzie, R.H.

1985-01-01

Rigorous results are given to the effect that a transparent gravitational lens produces an odd number of images. Suppose that p is an event and T the history of a light source in a globally hyperbolic space-time (M,g). Uhlenbeck's Morse theory of null geodesics is used to show under quite general conditions that if there are at most a finite number n of future-directed null geodesics from T to p, then M is contractible to a point. Moreover, n is odd and 1/2 (n-1) of the images of the source seen by an observer at p have the opposite orientation to the source. An analogous result is noted for Riemannian manifolds with positive definite metric

Killing vectors in algebraically special space-times

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1984-01-01

The form of the isometric, homothetic, and conformal Killing vectors for algebraically special metrics which admit a shear-free congruence of null geodesics is obtained by considering their complexification, using the existence of a congruence of null strings. The Killing equations are partially integrated and the reasons which permit this reduction are exhibited. In the case where the congruence of null strings has a vanishing expansion, the Killing equations are reduced to a single master equation

Motion of a spinning test particle in Vaidya's radiating metric

International Nuclear Information System (INIS)

Carmeli, M.; Charach, C.; Kaye, M.

1977-01-01

The motion of a spinning test particle in Vaidya's gravitational field is considered in the framework of Papapetrou's equations of motion. Use is made of the supplementary condition S/sup μ//sup u/ = 0, where u is the retarded Schwarzschild time coordinate. We derive the equations for the dynamical variables, and consider the conservation laws, that follow from the equations of motion. Particular cases of motion are also discussed and additional first integrals corresponding to these cases are found. Some of the new extra integrals are related to the Casimir operators of the Poincare group. It is found that under special conditions on the spin tensor components the particle follows a geodesic. Motion of the spinning test particle in the Schwarzschild field is considered as one of the particular cases

A hierarchical scheme for geodesic anatomical labeling of airway trees

DEFF Research Database (Denmark)

Feragen, Aasa; Petersen, Jens; Owen, Megan

2012-01-01

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

Introduction to general relativity

CERN Document Server

Parthasarthy, R

2016-01-01

INTRODUCTION TO GENERAL RELATIVITY begins with a description of the geometry of curved space, explaining geodesics, parallel transport, covariant differentiation, geodesic deviation and spacetime symmetry by killing vectors. It then introduces Einstein's theory of gravitation followed by Schwarzschild solution with its relevance to Positive Mass theorem. The three tests for Einstein's gravity are explained. Other exact solutions such as Vaidya, Kerr and Reisner - Nordstrom metric are included. In the Chapter on cosmological solutions, a detailed description of Godel metric is provided. It then introduces five dimensional spacetime of Kaluza showing the unification of gravity with electromagnetism. This is extended to include non-Abelian gauge theory by invoking compact extra dimensions. Explicit expressions in this case for Christoffel connections and ricci tensor are derived and the higher dimensional gravity action is shown to compactification are given.

Extremal surfaces and the rigidity of null geodesic incompleteness

International Nuclear Information System (INIS)

Silva, I P Costa e; Flores, J L

2015-01-01

An important, if relatively less well known aspect of the singularity theorems in Lorentzian geometry, is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified conclusion may arise, showing that those conclusions will fail only in special cases, at least some of which may be described. These are the so-called rigidity theorems, and have many important examples in the specialized literature. In this paper, we prove rigidity results for generalized plane waves and certain globally hyperbolic spacetimes in the presence of extremal compact surfaces. (paper)

Null infinity and extremal horizons in AdS-CFT

International Nuclear Information System (INIS)

Hickling, Andrew; Wiseman, Toby; Lucietti, James

2015-01-01

We consider AdS gravity duals to CFT on background spacetimes with a null infinity. Null infinity on the conformal boundary may extend to an extremal horizon in the bulk. For example it does so for Poincaré–AdS, although does not for planar Schwarzschild–AdS. If null infinity does extend into an extremal horizon in the bulk, we show that the bulk near-horizon geometry is determined by the geometry of the boundary null infinity. Hence the ‘infra-red’ geometry of the bulk is fixed by the large scale behaviour of the CFT spacetime. In addition the boundary stress tensor must have a particular decay at null infinity. As an application, we argue that for CFT on asymptotically flat backgrounds, any static bulk dual containing an extremal horizon extending from the boundary null infinity, must have the near-horizon geometry of Poincaré–AdS. We also discuss a class of boundary null infinity that cannot extend to a bulk extremal horizon, although we give evidence that they can extend to an analogous null surface in the bulk which possesses an associated scale-invariant ‘near-geometry’. (paper)

Null lifts and projective dynamics

Energy Technology Data Exchange (ETDEWEB)

Cariglia, Marco, E-mail: marco@iceb.ufop.br

2015-11-15

We describe natural Hamiltonian systems using projective geometry. The null lift procedure endows the tangent bundle with a projective structure where the null Hamiltonian is identified with a projective conic and induces a Weyl geometry. Projective transformations generate a set of known and new dualities between Hamiltonian systems, as for example the phenomenon of coupling-constant metamorphosis. We conclude outlining how this construction can be extended to the quantum case for Eisenhart–Duval lifts.

Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole

Directory of Open Access Journals (Sweden)

Alexis Larrañaga

2013-01-01

Full Text Available The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD. Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

The Importance of Proving the Null

Science.gov (United States)

Gallistel, C. R.

2009-01-01

Null hypotheses are simple, precise, and theoretically important. Conventional statistical analysis cannot support them; Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative, because the vaguer the alternative is (the more it spreads out the unit mass of prior probability), the more the null is…

Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation

International Nuclear Information System (INIS)

Hod, Shahar

2009-01-01

It has long been known that null unstable geodesics are related to the characteristic modes of black holes--the so-called quasinormal resonances. The basic idea is to interpret the free oscillations of a black hole in the eikonal limit in terms of null particles trapped at the unstable circular orbit and slowly leaking out. The real part of the complex quasinormal resonances is related to the angular velocity at the unstable null geodesic. The imaginary part of the resonances is related to the instability time scale (or the inverse Lyapunov exponent) of the orbit. While this geometric-optics description of the black-hole quasinormal resonances in terms of perturbed null rays is very appealing and intuitive, it is still highly important to verify the validity of this approach by directly analyzing the Teukolsky wave equation which governs the dynamics of perturbation waves in the black-hole spacetime. This is the main goal of the present paper. We first use the geometric-optics technique of perturbing a bundle of unstable null rays to calculate the resonances of near-extremal Kerr black holes in the eikonal approximation. We then directly solve the Teukolsky wave equation (supplemented by the appropriate physical boundary conditions) and show that the resultant quasinormal spectrum obtained directly from the wave analysis is in accord with the spectrum obtained from the geometric-optics approximation of perturbed null rays.

Relativistic gas in a Schwarzschild metric

International Nuclear Information System (INIS)

Kremer, Gilberto M

2013-01-01

A relativistic gas in a Schwarzschild metric is studied within the framework of a relativistic Boltzmann equation in the presence of gravitational fields, where Marle’s model for the collision operator of the Boltzmann equation is employed. The transport coefficients of the bulk and shear viscosities and thermal conductivity are determined from the Chapman–Enskog method. It is shown that the transport coefficients depend on the gravitational potential. Expressions for the transport coefficients in the presence of weak gravitational fields in the non-relativistic (low temperature) and ultra-relativistic (high temperature) limiting cases are given. Apart from the temperature gradient the heat flux has two relativistic terms. The first one, proposed by Eckart, is due to the inertia of energy and represents an isothermal heat flux when matter is accelerated. The other, suggested by Tolman, is proportional to the gravitational potential gradient and indicates that—in the absence of an acceleration field—a state of equilibrium of a relativistic gas in a gravitational field can be attained only if the temperature gradient is counterbalanced by a gravitational potential gradient. (paper)

Quantum tunneling effect of Dirac particles in a Schwarzschild-Godel space-time

Energy Technology Data Exchange (ETDEWEB)

Qi, D.-J.; Li, S.-M., E-mail: qidejiang0504@126.com [Shenyang Inst. of Engineering, Shenyang (China); Ru, H.-Q. [Northeastern Univ., Shenyang (China)

2010-11-15

In this paper, motivated by the Kerner and Man fermion tunneling method of 4-dimensional black holes, we further improve the analysis to investigate the quantum tunneling effect of Dirac particles from the five-dimensional Schwarzschild-Godel black hole. We successfully construct a set of appropriate matrices γ{sup μ} for the general covariant Dirac equation and derive the tunneling probability and Hawking temperature, which is exactly the same as that obtained by other methods. (author)

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

The Cardy-Verlinde formula and topological AdS-Schwarzschild black holes

International Nuclear Information System (INIS)

Youm, Donam

2001-05-01

We consider the brane universe in the background of the topological AdS-Schwarzschild black holes. The induced geometry of the brane is that of a flat or an open radiation dominated FRW-universe. Just like the case of a closed radiation dominated FRW-universe, the temperature and entropy are simply expressed in terms of the Hubble parameter and its time derivative when the brane crosses the black hole horizon. We propose the modified Cardy-Verlinde formula which is valid for any values of the curvature parameter k in the Friedmann equations. (author)

Cancellation of the central singularity of the Schwarzschild solution with natural mass inversion process

Science.gov (United States)

Petit, Jean-Pierre; D'Agostini, G.

2015-03-01

We reconsider the classical Schwarzschild solution in the context of a Janus cosmological model. We show that the central singularity can be eliminated through a simple coordinate change and that the subsequent transit from one fold to the other is accompanied by mass inversion. In such scenario matter swallowed by black holes could be ejected as invisible negative mass and dispersed in space.

Drift effects on electromagnetic geodesic acoustic modes

Energy Technology Data Exchange (ETDEWEB)

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

2015-02-15

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

Time travel in the homogeneous Som-Raychaudhuri Universe

International Nuclear Information System (INIS)

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

1987-01-01

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

Accelerating particles in general relativity (stationary C-metric)

International Nuclear Information System (INIS)

Farhoosh, H.

1979-01-01

The purpose of this thesis is to study the physical and geometrical properties of uniformly accelerating particles in the general theory of relativity and it consists of four main parts. In the first part the structure of the Killing horizons in the static vacuum C-metric which represents the gravitational field of a uniformly accelerating Schwarzschild like particle (non-rotating and spherically symmetric) is studied. In the second part these results are generalized to include the effects of the rotation of the source. For small acceleration and small rotation this solution reveals the existance of three Killing horizons. Two the these horizons are the Schwarzschild and the Rindler surfaces which are mainly due to the mass and the acceleration of the particle, respectively. In part three the radial geodesic and non-geodesic motions in the static vacuum C-metric (non-rotating case) are investigated. The effect of the dragging of the inertial frame is also shown in this part. In part four the radiative behavior of the stationary charged C-metric representing the electro-gravitational field of a uniformly accelerating and rotating charged particle with magnetic monopole and the NUT-parameter are investigated. The physical quantities - the news function, mass loss, mass, charge and the multipole moments - are calculated. It is also shown in this part that the magnetic monopole in the presence of rotation and acceleration affects the electric charge

ENERGY DISSIPATION IN MAGNETIC NULL POINTS AT KINETIC SCALES

International Nuclear Information System (INIS)

Olshevsky, Vyacheslav; Lapenta, Giovanni; Divin, Andrey; Eriksson, Elin; Markidis, Stefano

2015-01-01

We use kinetic particle-in-cell and MHD simulations supported by an observational data set to investigate magnetic reconnection in clusters of null points in space plasma. The magnetic configuration under investigation is driven by fast adiabatic flux rope compression that dissipates almost half of the initial magnetic field energy. In this phase powerful currents are excited producing secondary instabilities, and the system is brought into a state of “intermittent turbulence” within a few ion gyro-periods. Reconnection events are distributed all over the simulation domain and energy dissipation is rather volume-filling. Numerous spiral null points interconnected via their spines form null lines embedded into magnetic flux ropes; null point pairs demonstrate the signatures of torsional spine reconnection. However, energy dissipation mainly happens in the shear layers formed by adjacent flux ropes with oppositely directed currents. In these regions radial null pairs are spontaneously emerging and vanishing, associated with electron streams and small-scale current sheets. The number of spiral nulls in the simulation outweighs the number of radial nulls by a factor of 5–10, in accordance with Cluster observations in the Earth's magnetosheath. Twisted magnetic fields with embedded spiral null points might indicate the regions of major energy dissipation for future space missions such as the Magnetospheric Multiscale Mission

A geodesic atmospheric model with a quasi-Lagrangian vertical coordinate

International Nuclear Information System (INIS)

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

2006-01-01

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

An omnibus test for the global null hypothesis.

Science.gov (United States)

Futschik, Andreas; Taus, Thomas; Zehetmayer, Sonja

2018-01-01

Global hypothesis tests are a useful tool in the context of clinical trials, genetic studies, or meta-analyses, when researchers are not interested in testing individual hypotheses, but in testing whether none of the hypotheses is false. There are several possibilities how to test the global null hypothesis when the individual null hypotheses are independent. If it is assumed that many of the individual null hypotheses are false, combination tests have been recommended to maximize power. If, however, it is assumed that only one or a few null hypotheses are false, global tests based on individual test statistics are more powerful (e.g. Bonferroni or Simes test). However, usually there is no a priori knowledge on the number of false individual null hypotheses. We therefore propose an omnibus test based on cumulative sums of the transformed p-values. We show that this test yields an impressive overall performance. The proposed method is implemented in an R-package called omnibus.

Anomalies, effective action and Hawking temperatures of a Schwarzschild black hole in the isotropic coordinates

International Nuclear Information System (INIS)

Wu Shuangqing; Peng Junjin; Zhao Zhanyue

2008-01-01

Motivated by the universality of Hawking radiation and that of the anomaly cancellation technique as well as the effective action method, we investigate the Hawking radiation of a Schwarzschild black hole in the isotropic coordinates via the cancellation of gravitational anomaly. After performing a dimensional reduction from the four-dimensional isotropic Schwarzschild metric, we show that this reduction procedure will, in general, result in two classes of two-dimensional effective metrics: the conformal equivalent and the inequivalent ones. For the physically equivalent class, the two-dimensional effective metric displays such a distinct feature that the determinant is not equal to the unity √(-g)≠1, but also vanishes at the horizon, the latter of which possibly invalidates the anomaly analysis there. Nevertheless, in this paper we adopt the effective action method to prove that the consistent energy-momentum tensor T r t is divergent on the horizon but √(-g)T t r remains finite there. Meanwhile, through an explicit calculation we show that the covariant energy-momentum tensor T-tilde t r equals zero at the horizon. Therefore the validity of the covariant regularity condition that demands that T-tilde t r = 0 at the horizon has been justified, indicating that the gravitational anomaly analysis can be safely extrapolated to the case where the metric determinant vanishes at the horizon. It is then demonstrated that for the physically equivalent reduced metric, both methods can give the correct Hawking temperature of the isotropic Schwarzschild black hole, while for the inequivalent one with the determinant √(-g) = 1 it can only give half of the correct temperature. We further exclude the latter undesired result by taking into account the general covariance of the energy-momentum tensor under the isotropic coordinate transformation

Hawking radiation spectra for scalar fields by a higher-dimensional Schwarzschild-de Sitter black hole

Science.gov (United States)

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.

Effective temperatures and radiation spectra for a higher-dimensional Schwarzschild-de Sitter black hole

Science.gov (United States)

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.

Geodesic acoustic modes excited by finite beta drift waves

DEFF Research Database (Denmark)

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

2008-01-01

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

Nonlinear excitation of geodesic acoustic modes by drift waves

International Nuclear Information System (INIS)

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

2007-01-01

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

Null controllability of the viscous Camassa–Holm equation with ...

Indian Academy of Sciences (India)

In this paper, we study the null controllability of the viscous Camassa–. Holm equation on the one-dimensional torus. By using a moving distributed control, we obtain that the system is null controllable for a given data with certain regularity. Keywords. Viscous Camassa–Holm equation; null controllability; moving control;.

Null Subjects in European and Brazilian Portuguese

Directory of Open Access Journals (Sweden)

Pilar Barbosa

2005-12-01

Full Text Available The goals of this paper are twofold: a to provide a structural account of the effects of the informal ‘Avoid Pronoun Principle’, proposed in Chomsky (1981: 65 for the Null Subject Languages (NSLs, and b to compare, in European and Brazilian Portuguese (EP and BP, the distribution of the third person pronouns in its full and null forms, to check whether in written corpora BP incorporates signs of the ongoing loss of the null subject, largely attested in its contemporary spoken language. The strong theoretical claim is that in the Romance non-NSLs the pre-verbal subject is sitting in Spec of IP, while in the Romance NSLs it is Clitic Left-Dislocated (or is extracted by A-bar movement if it belongs to a restricted set of non-referential quantified expressions. The paper provides quantitative evidence that BP is losing the properties associated with the Null Subject Parameter. In its qualitative analysis, it shows that the contrasts between EP and BP are easily accounted for if the two derivations are assumed and if the null subjects in the two varieties are considered to be of a different nature: a pronoun in EP and a pronominal anaphor in BP.

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

International Nuclear Information System (INIS)

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

2009-01-01

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

Null-strut calculus. I. Kinematics

International Nuclear Information System (INIS)

Kheyfets, A.; LaFave, N.J.; Miller, W.A.

1990-01-01

This paper describes the kinematics of null-strut calculus---a 3+1 Regge calculus approach to general relativity. We show how to model the geometry of spacetime with simplicial spacelike three-geometries (TET's) linked to ''earlier'' and ''later'' momentumlike lattice surfaces (TET * ) entirely by light rays or ''null struts.'' These three-layered lattice spacetime geometries are defined and analyzed using combinatorial formulas for the structure of polytopes. The following paper in this series describes how these three-layered spacetime lattices are used to model spacetimes in full conformity with Einstein's theory of gravity

The Visible Nulling Coronagraph--Architecture Definition and Technology Development

Science.gov (United States)

Shao, Michael; Levine, B. Martin; Wallace, J. Kent; Liu, Duncan T.; Schmidtlin, Edouard; Serabyn, Eugene; Mennesson, Bertrand; Green, Joseph J.; Aguayo, Francisco; Fregoso, S. Felipe;

Self-force calculations with matched expansions and quasinormal mode sums

International Nuclear Information System (INIS)

Casals, Marc; Dolan, Sam; Ottewill, Adrian C.; Wardell, Barry

2009-01-01

Accurate modeling of gravitational wave emission by extreme-mass ratio inspirals is essential for their detection by the LISA mission. A leading perturbative approach involves the calculation of the self-force acting upon the smaller orbital body. In this work, we present the first application of the Poisson-Wiseman-Anderson method of 'matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function, which are, respectively, valid in the 'quasilocal' and 'distant past' regimes, and which may be matched together within the normal neighborhood. We perform our calculation in a static region of the spherically symmetric Nariai spacetime (dS 2 xS 2 ), in which scalar-field perturbations are governed by a radial equation with a Poeschl-Teller potential (frequently used as an approximation to the Schwarzschild radial potential) whose solutions are known in closed form. The key new ingredients in our study are (i) very high order quasilocal expansions and (ii) expansion of the distant past Green function in quasinormal modes. In combination, these tools enable a detailed study of the properties of the scalar-field Green function. We demonstrate that the Green function is singular whenever x and x ' are connected by a null geodesic, and apply asymptotic methods to determine the structure of the Green function near the null wave front. We show that the singular part of the Green function undergoes a transition each time the null wave front passes through a caustic point, following a repeating fourfold sequence δ(σ), 1/πσ, -δ(σ), -1/πσ, etc., where σ is Synge's world function. The matched-expansion method provides insight into the nonlocal properties of the self-force. We show that the self-force generated by the segment of the worldline lying outside the normal neighborhood is not negligible. We apply the matched-expansion method to compute the scalar self-force acting on

A Comparison of Plasma Performance Between Single-Null and Double-Null Configurations During Elming H-Mode

International Nuclear Information System (INIS)

Petrie, T.W.; Fenstermacher, M.E.; Allen, S.L.; Carlstrom, T.N.; Gohil, P.; Groebner, R.J.; Greenfield, C.M.; Hyatt, A.W.; Lasnier, C.J.; La Haye, R.J.; Leonard, A.W.; Mahdavi, M.A.; Osborne, T.H.; Porter, G.D.; Rhodes, T.L.; Thomas, D.M.; Watkins, J.G.; West, W.P.; Wolf, N.S.

1999-01-01

Tokamak plasma performance generally improves with increased shaping of the plasma cross section, such as higher elongation and higher triangularity. The stronger shaping, especially higher triangularity, leads to changes in the magnetic topology of the divertor. Because there are engineering and divertor physics issues associated with changes in the details of the divertor flux geometry, especially as the configuration transitions from a single-null (SN) divertor to a marginally balanced double-null (DN) divertor, we have undertaken a systematic evaluation of the plasma characteristics as the magnetic geometry is varied, particularly with respect to (1) energy confinement, (2) the response of the plasma to deuterium gas fueling, (3) the operational density range for the ELMing H-mode, and (4) heat flux sharing by the diverters. To quantify the degree of divertor imbalance (or equivalently, to what degree the shape is double-null or single-null), we define a parameter DRSEP. DRSEP is taken as the radial distance between the upper divertor separatrix and the lower divertor separatrix, as determined at the outboard midplane. For example, if DRSEP=O, the configuration is a magnetically balanced DN; if DRSEP = +1.0 cm, the divertor configuration is biased toward the upper divertor. Three examples are shown in Fig. 1. In the following discussions, VB drift is directed toward the lower divertor

Electromagnetic characteristics of geodesic acoustic mode in the COMPASS tokamak

Czech Academy of Sciences Publication Activity Database

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

2017-01-01

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

Accretion of new variable modified Chaplygin gas and generalized cosmic Chaplygin gas onto Schwarzschild and Kerr-Newman black holes

International Nuclear Information System (INIS)

Bhadra, Jhumpa; Debnath, Ujjal

2012-01-01

In this work, we have studied accretion of the dark energies in new variable modified Chaplygin gas (NVMCG) and generalized cosmic Chaplygin gas (GCCG) models onto Schwarzschild and Kerr-Newman black holes. We find the expression of the critical four velocity component which gradually decreases for the fluid flow towards the Schwarzschild as well as the Kerr-Newman black hole. We also find the expression for the change of mass of the black hole in both cases. For the Kerr-Newman black hole, which is rotating and charged, we calculate the specific angular momentum and total angular momentum. We showed that in both cases, due to accretion of dark energy, the mass of the black hole increases and angular momentum increases in the case of a Kerr-Newman black hole. (orig.)

CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking

Directory of Open Access Journals (Sweden)

Evert van Aart

2011-01-01

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

Quasilocal contribution to the scalar self-force: Geodesic motion

International Nuclear Information System (INIS)

Ottewill, Adrian C.; Wardell, Barry

2008-01-01

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

Fine art of computing nulling interferometer maps

Science.gov (United States)

Hénault, F.

2008-07-01

Spaceborne nulling interferometers are often characterized by means of their nulling ratio, which is defined as the deepest possible extinction of one target star supposed to harbor an extra-solar system. Herein is shown that another parameter, which is the transmitting efficiency of nearby bright fringes, is also of prime importance. More generally, "nulling maps" formed by the whole destructive and constructive fringe pattern projected on-sky, are found to be very sensitive on the design of some subsystems constituting the interferometer. In particular, we consider Spatial Filtering (SF) and Achromatic Phase Shifter (APS) devices, both required achieving planet detection and characterization. Consequences of the SF choice (pinhole or single-mode optical fiber) and APS properties (with or without induced pupil-flip) are discussed, for both monochromatic and polychromatic cases. Examples of numerical simulations are provided for single Bracewell interferometer, Angel cross and X-array configurations, demonstrating noticeable differences in the aspect of resulting nulling maps. It is concluded that both FS and APS designs exhibit variable capacities for serendipitous planet discovery.

Touching Ghosts: Observing Free Fall from an Infalling Frame of Reference into a Schwarzschild Black Hole

Science.gov (United States)

Augousti, A. T.; Gawelczyk, M.; Siwek, A.; Radosz, A.

2012-01-01

The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mother station (MS) is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are…

Calculating observables in inhomogeneous cosmologies. Part I: general framework

Science.gov (United States)

Hellaby, Charles; Walters, Anthony

2018-02-01

We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift, proper motions, area distance and redshift-space density. Of particular interest are observables that are zero in the spherically symmetric case, such as proper motions. The algorithm is based on the null geodesic equation and the geodesic deviation equation, and it is tailored to creating a practical numerical implementation. The algorithm provides a method for tracking which light rays connect moving objects to the observer at successive times. Our algorithm is applied to the particular case of the Szekeres metric. A numerical implementation has been created and some results will be presented in a subsequent paper. Future work will explore the range of possibilities.

Latex allergy and filaggrin null mutations

DEFF Research Database (Denmark)

Carlsen, Berit C; Meldgaard, Michael; Hamann, Dathan

2011-01-01

to aeroallergens and it is possible that filaggrin null mutations also increase the risk of latex allergy. The aim of this paper was to examine the association between filaggrin null mutations and type I latex allergy. Methods Twenty latex allergic and 24 non-latex allergic dentists and dental assistants...... in the cases in this study may not have occurred through direct skin contact but through the respiratory organs via latex proteins that are absorbed in glove powder and aerosolized...

Mode coupling of Schwarzschild perturbations: Ringdown frequencies

International Nuclear Information System (INIS)

Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel

2010-01-01

Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.

Qualification of a Null Lens Using Image-Based Phase Retrieval

Science.gov (United States)

Bolcar, Matthew R.; Aronstein, David L.; Hill, Peter C.; Smith, J. Scott; Zielinski, Thomas P.

2012-01-01

In measuring the figure error of an aspheric optic using a null lens, the wavefront contribution from the null lens must be independently and accurately characterized in order to isolate the optical performance of the aspheric optic alone. Various techniques can be used to characterize such a null lens, including interferometry, profilometry and image-based methods. Only image-based methods, such as phase retrieval, can measure the null-lens wavefront in situ - in single-pass, and at the same conjugates and in the same alignment state in which the null lens will ultimately be used - with no additional optical components. Due to the intended purpose of a Dull lens (e.g., to null a large aspheric wavefront with a near-equal-but-opposite spherical wavefront), characterizing a null-lens wavefront presents several challenges to image-based phase retrieval: Large wavefront slopes and high-dynamic-range data decrease the capture range of phase-retrieval algorithms, increase the requirements on the fidelity of the forward model of the optical system, and make it difficult to extract diagnostic information (e.g., the system F/#) from the image data. In this paper, we present a study of these effects on phase-retrieval algorithms in the context of a null lens used in component development for the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission. Approaches for mitigation are also discussed.

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

International Nuclear Information System (INIS)

Singh, Rameswar; Gurcan, Ozgur D.

2015-01-01

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

Evaluation of null-point detection methods on simulation data

Science.gov (United States)

Olshevsky, Vyacheslav; Fu, Huishan; Vaivads, Andris; Khotyaintsev, Yuri; Lapenta, Giovanni; Markidis, Stefano

2014-05-01

We model the measurements of artificial spacecraft that resemble the configuration of CLUSTER propagating in the particle-in-cell simulation of turbulent magnetic reconnection. The simulation domain contains multiple isolated X-type null-points, but the majority are O-type null-points. Simulations show that current pinches surrounded by twisted fields, analogous to laboratory pinches, are formed along the sequences of O-type nulls. In the simulation, the magnetic reconnection is mainly driven by the kinking of the pinches, at spatial scales of several ion inertial lentghs. We compute the locations of magnetic null-points and detect their type. When the satellites are separated by the fractions of ion inertial length, as it is for CLUSTER, they are able to locate both the isolated null-points, and the pinches. We apply the method to the real CLUSTER data and speculate how common are pinches in the magnetosphere, and whether they play a dominant role in the dissipation of magnetic energy.

3rd Karl Schwarzschild Meeting - Gravity and the Gauge/Gravity Correspondence

Science.gov (United States)

Nicolini, Piero; Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus

2018-01-01

The Karl Schwarzschild Meeting 2017 (KSM2017) has been the third instalment of the conference dedicated to the great Frankfurter scientist, who derived the first black hole solution of Einstein's equations about 100 years ago. The event has been a 5 day meeting in the field of black holes, AdS/CFT correspondence and gravitational physics. Like the two previous instalments, the conference continued to attract a stellar ensemble of participants from the world's most renowned institutions. The core of the meeting has been a series of invited talks from eminent experts (keynote speakers) as well as the presence of plenary research talks by students and junior speakers.

Phase-space lagrangians for null spinning strings

International Nuclear Information System (INIS)

Barcelos-Neto, J.; Ruiz-Altaba, M.; Ramirez, C.

1990-01-01

The striking fact that normal-ordered null strings have the same critical dimension as their usual non-zero tension siblings can be understood from the observation that one must, in the tensionless case, keep all the conjugate momenta as independent dynamical variables, thus doubling the number of physical degrees of freedom. The fermionic momenta give rise to a second-class constraint which cannot be solved covariantly, but can be successfully incorporated into the first-class constraint algebra after gauge-fixing. The ghost contributions to the anomaly consist of two b-c (and also two β-γ systems in the supersymmetric case), of the single Virasoro sub(super)algebra for the closed null (spinning) string. In the appropriate gauge, the null (super)string is (super)chiral. (orig.)

On the world function of the Schwarzschild field

International Nuclear Information System (INIS)

Buchdahl, H.A.; Warner, N.P.

1979-01-01

The representation of the world function Ω of the Schwarzschild field as a power series is investigated. The initial concern is with a neighbourhood of the event horizon. The symmetries of the metric are invoked effectively to reduce the number of independent variables upon which Ω depends from eight to four, and to show that when these are sufficiently small in magnitude Ω is an analytic function of them. A fairly large number of the early terms of the power series for Ω is found explicitly. The condition that one is to remain sufficiently close to the event horizon is then relaxed, it being merely stipulated that the endpoints shall be sufficiently close to each other. Finally, using other variables, the early terms of a series for Ω are obtained for the case in which the endpoints are restricted to lie outside the event horizon and sufficiently close to each other. (author)

High overtones of Schwarzschild-de-Sitter quasinormal spectrum

International Nuclear Information System (INIS)

Konoplya, R.A.; Zhidenko, A.

2004-01-01

We find the high overtones of gravitational and electromagnetic quasinormal spectrum of the Schwarzschild-de Sitter black hole. The calculations show that the real parts of the electromagnetic modes asymptotically approach zero. The gravitational modes show more peculiar behavior at large n: the real part oscillates as a function of imaginary even for very high overtones and these oscillations settles to some 'profile' which just repeats itself with further increasing of the overtone number n. This lets us judge that Reω is not a constant as n →∞ but rather some oscillating function. The spacing for imaginary part Imω n+1 -Imω n for electromagnetic perturbations at high n slowly approach k e as n→∞, where k e is the surface gravity. In addition we find the lower QN modes for which the values obtained with numerical methods are in a very good agreement with those obtained through the 6th order WKB technique. (author)

Charged fluids with symmetries

Indian Academy of Sciences (India)

It is possible to introduce many types of symmetries on the manifold which restrict the ... metric tensor field and generate constants of the motion along null geodesics .... In this analysis we have studied the role of symmetries for charged perfect ...

Tensionless branes and the null string critical dimension

International Nuclear Information System (INIS)

Bozhilov, P.

1998-01-01

BRST quantization is carried out for a model of p-branes with second class constraints. After extension of the phase space the constraint algebra coincides with the one of null string when p=1. It is shown that in this case one can or cannot obtain critical dimension for the null string, depending on the choice of the operator ordering and corresponding vacuum states. When p>1, operator orderings leading to critical dimension in the p=1 case are not allowed. Admissible orderings give no restrictions on the dimension of the embedding space-time. Finally, a generalization to supersymmetric null branes is proposed

Algebraically special perturbations of the Schwarzschild solution in higher dimensions

International Nuclear Information System (INIS)

Dias, Óscar J C; Reall, Harvey S

2013-01-01

We study algebraically special perturbations of a generalized Schwarzschild solution in any number of dimensions. There are two motivations. First, to learn whether there exist interesting higher-dimensional algebraically special solutions beyond the known ones. Second, algebraically special perturbations present an obstruction to the unique reconstruction of general metric perturbations from gauge-invariant variables analogous to the Teukolsky scalars and it is desirable to know the extent of this non-uniqueness. In four dimensions, our results generalize those of Couch and Newman, who found infinite families of time-dependent algebraically special perturbations. In higher dimensions, we find that the only regular algebraically special perturbations are those corresponding to deformations within the Myers–Perry family. Our results are relevant for several inequivalent definitions of ‘algebraically special’. (paper)

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

International Nuclear Information System (INIS)

Dappiaggi, Claudio; Pinamonti, Nicola

2009-07-01

The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hoermander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime. (orig.)

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Energy Technology Data Exchange (ETDEWEB)

Dappiaggi, Claudio; Pinamonti, Nicola [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Moretti, Valter [Trento Univ., Povo (Italy). Dipt. di Matematica; Istituto Nazionale di Fisica Nucleare, Povo (Italy); Istituto Nazionale di Alta Matematica ' ' F. Severi' ' , GNFM, Sesto Fiorentino (Italy)

2009-07-15

The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hoermander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime. (orig.)

Resistivity at the field null of the FRC plasma

International Nuclear Information System (INIS)

Gerwin, R.A.

1989-01-01

In the absence of the major destructive instabilities, the configuration time is ultimately determined by particle and flux containment. If the profiles are ''gentle,'' then the anomalous flux-loss rate depends essentially on the anomalous resistivity at the field null. Conventional electrostatic quasi-linear models of anomalous cross-field resistive diffusivity are based upon the use of rvec E x rvec B drift velocities, and hence break down at the magnetic field null. In this paper, an electromagnetic treatment valid at the field null is developed, based upon the presence of flute-parity perturbations. An expression for anomalous resistivity at the field null in the quasi-linear approximation is derived by averaging in the ignorable direction over the random phases of the perturbations. The expression is valid for arbitrary (non-local) radial shapes of the perturbing modes (for example, the eigenfunctions need not be centered at the field null), and for an arbitrary ratio of real frequency to growth rate. The effective resistivity due to flute perturbations of the MHD type will be considered. 1 ref

Liouville's equation and radiative acceleration in general relativity

International Nuclear Information System (INIS)

Keane, A.J.

1999-01-01

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

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

Science.gov (United States)

Zarrinpanjeh, N.; Dadrassjavan, F.

2017-09-01

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

Thermodynamics of the Schwarzschild-de Sitter black hole: Thermal stability of the Nariai black hole

International Nuclear Information System (INIS)

Myung, Yun Soo

2008-01-01

We study the thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization and does not favor the Bousso-Hawking normalization

Quadratic curvature terms and deformed Schwarzschild–de Sitter black hole analogues in the laboratory

Directory of Open Access Journals (Sweden)

R. da Rocha

2017-12-01

Full Text Available Sound waves on a fluid stream, in a de Laval nozzle, are shown to correspond to quasinormal modes emitted by black holes that are physical solutions in a quadratic curvature gravity with cosmological constant. Sound waves patterns in transsonic regimes at a laboratory are employed here to provide experimental data regarding generalized theories of gravity, comprised by the exact de Sitter-like solution and a perturbative solution around the Schwarzschild–de Sitter standard solution as well. Using the classical tests of General Relativity to bound free parameters in these solutions, acoustic perturbations on fluid flows in nozzles are then regarded, to study quasinormal modes of these black holes solutions, providing deviations of the de Laval nozzle cross-sectional area, when compared to the Schwarzschild solution. The fluid sonic point in the nozzle, for sound waves in the fluid, is shown to implement the acoustic event horizon corresponding to quasinormal modes. Keywords: Black holes, Fluid branes, Fluid dynamics, Quadratic curvature gravity, de Laval nozzle

A detailed analytic study of the asymptotic quasinormal modes of Schwarzschild-anti de Sitter black holes

International Nuclear Information System (INIS)

Daghigh, Ramin G; Green, Michael D

2009-01-01

We analyze analytically the asymptotic regions of the quasinormal mode frequency spectra with infinitely large overtone numbers for D-dimensional Schwarzschild black holes in anti de Sitter spacetimes. In this limit, we confirm the analytic results obtained previously in the literature using different methods. In addition, we show that in certain spacetime dimensions these techniques imply the existence of other regions of the asymptotic quasinormal mode frequency spectrum which have not previously appeared in the literature. For large black holes, some of these modes have a damping rate of 1.2T H , where T H is the Hawking temperature. This is less than the damping rate of the lowest overtone quasinormal mode calculated by other authors. It is not completely clear whether these modes actually exist or are an artifact of an unknown flaw in the analytic techniques being used. We discuss the possibility of the existence of these modes and explore some of the consequences. We also examine the possible connection between the asymptotic quasinormal modes of Schwarzschild-anti de Sitter black holes and the quantum level spacing of their horizon area spectrum.

Matter sources for a null big bang

International Nuclear Information System (INIS)

Bronnikov, K A; Zaslavskii, O B

2008-01-01

We consider the properties of stress-energy tensors compatible with a null big bang, i.e., cosmological evolution starting from a Killing horizon rather than a singularity. For Kantowski-Sachs cosmologies, it is shown that if matter satisfies the null energy condition, then (i) regular cosmological evolution can only start from a Killing horizon, (ii) matter is absent at the horizon and (iii) matter can only appear in the cosmological region due to interaction with vacuum. The latter is understood phenomenologically as a fluid whose stress tensor is insensitive to boosts in a particular direction. We also argue that matter is absent in a static region beyond the horizon. All this generalizes the observations recently obtained for a mixture of dust and a vacuum fluid. If, however, we admit the existence of phantom matter, its certain special kinds (with the parameter w ≤ -3) are consistent with a null big bang without interaction with vacuum (or without vacuum fluid at all). Then in the static region there is matter with w ≥ -1/3. Alternatively, the evolution can begin from a horizon in an infinitely remote past, leading to a scenario combining the features of a null big bang and an emergent universe

GEODESIC RECONSTRUCTION, SADDLE ZONES & HIERARCHICAL SEGMENTATION

Directory of Open Access Journals (Sweden)

Serge Beucher

2011-05-01

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

New method for determining the light travel time in static, spherically symmetric spacetimes. Calculation of the terms of order G3

International Nuclear Information System (INIS)

Linet, Bernard; Teyssandier, Pierre

2013-01-01

A new iterative method for calculating the travel time of a photon as a function of the spatial positions of the emitter and the receiver in the field of a static, spherically symmetric body is presented. The components of the metric are assumed to be expressible in power series in m/r, with m being half the Schwarzschild radius of the central body and r a radial coordinate. The procedure exclusively works for a light ray which may be described as a perturbation in powers of G of a Minkowskian null geodesic, with G being the Newtonian gravitational constant. It is shown that the expansion of the travel time of a photon along such a ray only involves elementary integrals whatever the order of approximation. An expansion of the impact parameter in power series of G is also obtained. The method is applied to explicitly calculate the perturbation expansions of the light travel time and the impact parameter up to the third order. The full expression yielding the terms of order G 3 is new. This expression confirms the existence of a third-order enhanced term when the emitter and the receiver are in conjunction relative to the central body. This term is shown to be necessary for determining the post-Newtonian parameter γ at a level of accuracy of 10 −8 with light rays grazing the Sun. (paper)

Gravitational waveforms from a point particle orbiting a Schwarzschild black hole

International Nuclear Information System (INIS)

Martel, Karl

2004-01-01

We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations in the time domain. We obtain the gravitational waveforms produced by a point particle of mass μ traveling around a Schwarzschild black hole of mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular momentum at infinity and the event horizon are also calculated. Results for circular orbits, selected cases of eccentric orbits, and parabolic orbits are presented. The numerical results from the time-domain code indicate that, for all three types of orbital motion, black hole absorption contributes less than 1% of the total flux, so long as the orbital radius r p (t) satisfies r p (t)>5M at all times

K. Schwarzschild's problem in radiation transfer theory

International Nuclear Information System (INIS)

Rutily, B.; Chevallier, L.; Pelkowski, J.

2006-01-01

We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem-to be more precise the calculation of the source function within the slab-was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case (albedo=1), which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce (1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it (2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere

Tolerance analysis of null lenses using an end-use system performance criterion

Science.gov (United States)

Rodgers, J. Michael

2000-07-01

An effective method of assigning tolerances to a null lens is to determine the effects of null-lens fabrication and alignment errors on the end-use system itself, not simply the null lens. This paper describes a method to assign null- lens tolerances based on their effect on any performance parameter of the end-use system.

On extracting physical content from asymptotically flat spacetime metrics

International Nuclear Information System (INIS)

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

2008-01-01

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

Rational first integrals of geodesic equations and generalised hidden symmetries

International Nuclear Information System (INIS)

Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

2016-01-01

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

Solutions of the spin coefficient equations with nongeodesic eigenrays

International Nuclear Information System (INIS)

Kota, J.; Lukacs, B.; Perjes, Z.

1982-01-01

Among the many significant results obtained by spin coefficient techniques in general relativity, the exact integrals of gravitational equations have enjoyed particular attention. These integration procedures were first carried out with respect to a congruence of null geodesic curves. The authors show that spin coefficient equations can sometimes be exactly solved when the selected null congruence is nongeodesic. They derive metrics with this property and, among them, a new solution of the coupled Einstein-Maxwell equations. (Auth.)

Embeddings for the Schwarzschild metric: classification and new results

International Nuclear Information System (INIS)

Paston, S A; Sheykin, A A

2012-01-01

We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings of the Schwarzschild metric which have the symmetry of this solution, and all such embeddings in a six-dimensional ambient space (i.e. a space with a minimal possible dimension) are constructed. Four of the six possible embeddings are already known, while the two others are new. One of the new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be of use in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space. (paper)

Premeiotic germ cell defect in seminiferous tubules of Atm-null testis

International Nuclear Information System (INIS)

Takubo, Keiyo; Hirao, Atsushi; Ohmura, Masako; Azuma, Masaki; Arai, Fumio; Nagamatsu, Go; Suda, Toshio

2006-01-01

Lifelong spermatogenesis is maintained by coordinated sequential processes including self-renewal of stem cells, proliferation of spermatogonial cells, meiotic division, and spermiogenesis. It has been shown that ataxia telangiectasia-mutated (ATM) is required for meiotic division of the seminiferous tubules. Here, we show that, in addition to its role in meiosis, ATM has a pivotal role in premeiotic germ cell maintenance. ATM is activated in premeiotic spermatogonial cells and the Atm-null testis shows progressive degeneration. In Atm-null testicular cells, differing from bone marrow cells of Atm-null mice, reactive oxygen species-mediated p16 Ink4a activation does not occur in Atm-null premeiotic germ cells, which suggests the involvement of different signaling pathways from bone marrow defects. Although Atm-null bone marrow undergoes p16 Ink4a -mediated cellular senescence program, Atm-null premeiotic germ cells exhibited cell cycle arrest and apoptotic elimination of premeiotic germ cells, which is different from p16 Ink4a -mediated senescence

Revisiting event horizon finders

International Nuclear Information System (INIS)

Cohen, Michael I; Pfeiffer, Harald P; Scheel, Mark A

2009-01-01

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to find event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time is most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10 5 . Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only some of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.

Variational principle for gravity with null and non-null boundaries: a unified boundary counter-term

Energy Technology Data Exchange (ETDEWEB)

Parattu, Krishnamohan; Chakraborty, Sumanta; Padmanabhan, T. [IUCAA, Post Bag 4, Pune (India)

2016-03-15

It is common knowledge that the Einstein-Hilbert action does not furnish a well-posed variational principle. The usual solution to this problem is to add an extra boundary term to the action, called a counter-term, so that the variational principle becomes well-posed. When the boundary is spacelike or timelike, the Gibbons-Hawking-York counter-term is the most widely used. For null boundaries, we had proposed a counter-term in a previous paper. In this paper, we extend the previous analysis and propose a counter-term that can be used to eliminate variations of the ''off-the-surface'' derivatives of the metric on any boundary, regardless of its spacelike, timelike or null nature. (orig.)

Visible nulling coronagraphy testbed development for exoplanet detection

Science.gov (United States)

Lyon, Richard G.; Clampin, Mark; Woodruff, Robert A.; Vasudevan, Gopal; Thompson, Patrick; Chen, Andrew; Petrone, Peter; Booth, Andrew; Madison, Timothy; Bolcar, Matthew; Noecker, M. Charley; Kendrick, Stephen; Melnick, Gary; Tolls, Volker

2010-07-01

Three of the recently completed NASA Astrophysics Strategic Mission Concept (ASMC) studies addressed the feasibility of using a Visible Nulling Coronagraph (VNC) as the prime instrument for exoplanet science. The VNC approach is one of the few approaches that works with filled, segmented and sparse or diluted aperture telescope systems and thus spans the space of potential ASMC exoplanet missions. NASA/Goddard Space Flight Center (GSFC) has a well-established effort to develop VNC technologies and has developed an incremental sequence of VNC testbeds to advance the this approach and the technologies associated with it. Herein we report on the continued development of the vacuum Visible Nulling Coronagraph testbed (VNT). The VNT is an ultra-stable vibration isolated testbed that operates under high bandwidth closed-loop control within a vacuum chamber. It will be used to achieve an incremental sequence of three visible light nulling milestones of sequentially higher contrasts of 108, 109 and 1010 at an inner working angle of 2*λ/D and ultimately culminate in spectrally broadband (>20%) high contrast imaging. Each of the milestones, one per year, is traceable to one or more of the ASMC studies. The VNT uses a modified Mach-Zehnder nulling interferometer, modified with a modified "W" configuration to accommodate a hex-packed MEMS based deformable mirror, a coherent fiber bundle and achromatic phase shifters. Discussed will be the optical configuration laboratory results, critical technologies and the null sensing and control approach.

Scalar field dark matter: behavior around black holes

Energy Technology Data Exchange (ETDEWEB)

Cruz-Osorio, Alejandro; Guzmán, F. Siddhartha; Lora-Clavijo, Fabio D., E-mail: alejandro@ifm.umich.mx, E-mail: guzman@ifm.umich.mx, E-mail: fadulora@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán (Mexico)

2011-06-01

We present the numerical evolution of a massive test scalar fields around a Schwarzschild space-time. We proceed by using hyperboloidal slices that approach future null infinity, which is the boundary of scalar fields, and also demand the slices to penetrate the event horizon of the black hole. This approach allows the scalar field to be accreted by the black hole and to escape toward future null infinity. We track the evolution of the energy density of the scalar field, which determines the rate at which the scalar field is being diluted. We find polynomial decay of the energy density of the scalar field, and use it to estimate the rate of dilution of the field in time. Our findings imply that the energy density of the scalar field decreases even five orders of magnitude in time scales smaller than a year. This implies that if a supermassive black hole is the Schwarzschild solution, then scalar field dark matter would be diluted extremely fast.

Scalar field dark matter: behavior around black holes

International Nuclear Information System (INIS)

Cruz-Osorio, Alejandro; Guzmán, F. Siddhartha; Lora-Clavijo, Fabio D.

2011-01-01

We present the numerical evolution of a massive test scalar fields around a Schwarzschild space-time. We proceed by using hyperboloidal slices that approach future null infinity, which is the boundary of scalar fields, and also demand the slices to penetrate the event horizon of the black hole. This approach allows the scalar field to be accreted by the black hole and to escape toward future null infinity. We track the evolution of the energy density of the scalar field, which determines the rate at which the scalar field is being diluted. We find polynomial decay of the energy density of the scalar field, and use it to estimate the rate of dilution of the field in time. Our findings imply that the energy density of the scalar field decreases even five orders of magnitude in time scales smaller than a year. This implies that if a supermassive black hole is the Schwarzschild solution, then scalar field dark matter would be diluted extremely fast

Meterwavelength Single-pulse Polarimetric Emission Survey. III. The Phenomenon of Nulling in Pulsars

Energy Technology Data Exchange (ETDEWEB)

Basu, Rahul; Mitra, Dipanjan; Melikidze, George I., E-mail: rahulbasu.astro@gmail.com [Janusz Gil Institute of Astronomy, University of Zielona Góra, ul. Szafrana 2, 65–516 Zielona Góra (Poland)

2017-09-10

A detailed analysis of nulling was conducted for the pulsars studied in the Meterwavelength Single-pulse Polarimetric Emission Survey. We characterized nulling in 36 pulsars including 17 pulsars where the phenomenon was reported for the first time. The most dominant nulls lasted for a short duration, less than five periods. Longer duration nulls extending to hundreds of periods were also seen in some cases. A careful analysis showed the presence of periodicities in the transition from the null to the burst states in 11 pulsars. In our earlier work, fluctuation spectrum analysis showed multiple periodicities in 6 of these 11 pulsars. We demonstrate that the longer periodicity in each case was associated with nulling. The shorter periodicities usually originate from subpulse drifting. The nulling periodicities were more aligned with the periodic amplitude modulation, indicating a possible common origin for both. The most prevalent nulls last for a single period and can be potentially explained using random variations affecting the plasma processes in the pulsar magnetosphere. On the other hand, longer-duration nulls require changes in the pair-production processes, which need an external triggering mechanism for the changes. The presence of periodic nulling puts an added constraint on the triggering mechanism, which also needs to be periodic.

Emission and null coordinates: geometrical properties and physical construction

International Nuclear Information System (INIS)

Coll, Bartolome; Ferrando, Joan J; Morales-Lladosa, Juan A

2011-01-01

A Relativistic Positioning System is defined by four clocks (emitters) broadcasting their proper time. Then, every event reached by the signals is naturally labeled by these four times which are the emission coordinates of this event. The coordinate hypersurfaces of the emission coordinates are the future light cones based on the emitter trajectories. For this reason the emission coordinates have been also named null coordinates or light coordinates. Nevertheless, other coordinate systems used in different relativistic contexts have the own right to be named null or light coordinates. Here we analyze when one can say that a coordinate is a null coordinate and when one can say that a coordinate system is null. Moreover, we examine the physical construction and the geometrical properties of several n ull coordinate systems : the emission and the reception coordinates, the radar coordinates, and the Bondi-Sachs coordinates, among others.

Shocks and currents in stratified atmospheres with a magnetic null point

Science.gov (United States)

Tarr, Lucas A.; Linton, Mark

2017-08-01

We use the resistive MHD code LARE (Arber et al 2001) to inject a compressive MHD wavepacket into a stratified atmosphere that has a single magnetic null point, as recently described in Tarr et al 2017. The 2.5D simulation represents a slice through a small ephemeral region or area of plage. The strong gradients in field strength and connectivity related to the presence of the null produce substantially different dynamics compared to the more slowly varying fields typically used in simple sunspot models. The wave-null interaction produces a fast mode shock that collapses the null into a current sheet and generates a set of outward propagating (from the null) slow mode shocks confined to field lines near each separatrix. A combination of oscillatory reconnection and shock dissipation ultimately raise the plasma's internal energy at the null and along each separatrix by 25-50% above the background. The resulting pressure gradients must be balanced by Lorentz forces, so that the final state has contact discontinuities along each separatrix and a persistent current at the null. The simulation demonstrates that fast and slow mode waves localize currents to the topologically important locations of the field, just as their Alfvenic counterparts do, and also illustrates the necessity of treating waves and reconnection as coupled phenomena.

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

International Nuclear Information System (INIS)

Schubert, R.

1995-05-01

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

Influence of the cosmological constant on gravitational lensing in small systems

International Nuclear Information System (INIS)

Sereno, Mauro

2008-01-01

The cosmological constant Λ affects gravitational lensing phenomena. The contribution of Λ to the observable angular positions of multiple images and to their amplification and time delay is here computed through a study of the weak deflection limit of the equations of motion in the Schwarzschild-de Sitter metric. Because of Λ the unresolved images are slightly demagnified, the radius of the Einstein ring decreases, and the time delay increases. The effect is however negligible for near lenses. In the case of a null cosmological constant, we provide some updated results on lensing by a Schwarzschild black hole

Non-Gaussian ground-state deformations near a black-hole singularity

Science.gov (United States)

Hofmann, Stefan; Schneider, Marc

2017-03-01

The singularity theorem by Hawking and Penrose qualifies Schwarzschild black holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows us to probe the spacelike singularity via a measurement process. Any such framework necessarily has to be based on quantum theory. As a consequence, the notion of classical completeness needs to be adapted to situations where the only adequate description is in terms of quantum fields in dynamical space-times. It is shown that Schwarzschild black holes turn out to be complete when probed by self-interacting quantum fields in the ground state and in excited states. The measure for populating quantum fields on hypersurfaces in the vicinity of the black-hole singularity goes to zero towards the singularity. This statement is robust under non-Gaussian deformations of and excitations relative to the ground state. The physical relevance of different completeness concepts for black holes is discussed.

Nonsingular black hole

Energy Technology Data Exchange (ETDEWEB)

Chamseddine, Ali H. [American University of Beirut, Physics Department, Beirut (Lebanon); I.H.E.S., Bures-sur-Yvette (France); Mukhanov, Viatcheslav [Niels Bohr Institute, Niels Bohr International Academy, Copenhagen (Denmark); Ludwig-Maximilians University, Theoretical Physics, Munich (Germany); MPI for Physics, Munich (Germany)

2017-03-15

We consider the Schwarzschild black hole and show how, in a theory with limiting curvature, the physical singularity ''inside it'' is removed. The resulting spacetime is geodesically complete. The internal structure of this nonsingular black hole is analogous to Russian nesting dolls. Namely, after falling into the black hole of radius r{sub g}, an observer, instead of being destroyed at the singularity, gets for a short time into the region with limiting curvature. After that he re-emerges in the near horizon region of a spacetime described by the Schwarzschild metric of a gravitational radius proportional to r{sub g}{sup 1/3}. In the next cycle, after passing the limiting curvature, the observer finds himself within a black hole of even smaller radius proportional to r{sub g}{sup 1/9}, and so on. Finally after a few cycles he will end up in the spacetime where he remains forever at limiting curvature. (orig.)

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

DEFF Research Database (Denmark)

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

2009-01-01

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

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

DEFF Research Database (Denmark)

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

2010-01-01

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

Magnetoacoustic Waves in a Stratified Atmosphere with a Magnetic Null Point

Energy Technology Data Exchange (ETDEWEB)

Tarr, Lucas A.; Linton, Mark; Leake, James, E-mail: lucas.tarr.ctr@nrl.navy.mil [U.S. Naval Research Laboratory, 4555 Overlook Ave. SW, Washington, DC 20375 (United States)

2017-03-01

We perform nonlinear MHD simulations to study the propagation of magnetoacoustic waves from the photosphere to the low corona. We focus on a 2D system with a gravitationally stratified atmosphere and three photospheric concentrations of magnetic flux that produce a magnetic null point with a magnetic dome topology. We find that a single wavepacket introduced at the lower boundary splits into multiple secondary wavepackets. A portion of the packet refracts toward the null owing to the varying Alfvén speed. Waves incident on the equipartition contour surrounding the null, where the sound and Alfvén speeds coincide, partially transmit, reflect, and mode-convert between branches of the local dispersion relation. Approximately 15.5% of the wavepacket’s initial energy ( E {sub input}) converges on the null, mostly as a fast magnetoacoustic wave. Conversion is very efficient: 70% of the energy incident on the null is converted to slow modes propagating away from the null, 7% leaves as a fast wave, and the remaining 23% (0.036 E {sub input}) is locally dissipated. The acoustic energy leaving the null is strongly concentrated along field lines near each of the null’s four separatrices. The portion of the wavepacket that refracts toward the null, and the amount of current accumulation, depends on the vertical and horizontal wavenumbers and the centroid position of the wavepacket as it crosses the photosphere. Regions that refract toward or away from the null do not simply coincide with regions of open versus closed magnetic field or regions of particular field orientation. We also model wavepacket propagation using a WKB method and find that it agrees qualitatively, though not quantitatively, with the results of the numerical simulation.

A new dynamic null model for phylogenetic community structure

NARCIS (Netherlands)

Pigot, Alex L; Etienne, Rampal S

Phylogenies are increasingly applied to identify the mechanisms structuring ecological communities but progress has been hindered by a reliance on statistical null models that ignore the historical process of community assembly. Here, we address this, and develop a dynamic null model of assembly by

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

Directory of Open Access Journals (Sweden)

N. Zarrinpanjeh

2017-09-01

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

Analytic continuation of tgensor fields along geodesics by covariant Taylor series

International Nuclear Information System (INIS)

Tsirulev, A.N.

1995-01-01

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

Explanation of Rotation Curves in Galaxies and Clusters of them, by Generalization of Schwarzschild Metric and Combination with MOND, eliminating Dark Matter

Science.gov (United States)

Vossos, Spyridon; Vossos, Elias

2017-12-01

Schwarzschild Metric is the first and the most important solution of Einstein vacuum field equations. This is associated with Lorentz metric of flat spacetime and produces the relativistic potential (Φ) and the field strength (g) outside a spherically symmetric mass or a non-rotating black hole. It has many applications such as gravitational red shift, the precession of Mercury’s orbit, Shapiro time delay etc. However, it is inefficient to explain the rotation curves in large galaxies and clusters of them, causing the necessity for dark matter. On the other hand, Modified Newtonian Dynamics (MOND) has already explained these rotation curves in many cases, using suitable interpolating function (μ) in Milgrom’s Law. In this presentation, we initially produce a Generalized Schwarzschild potential and the corresponding Metric of spacetime, in order to be in accordance with any isotropic metric of flat spacetime (including Galilean Metric of spacetime which is associated with Galilean Transformation of spacetime). From this Generalized Schwarzschild potential (Φ), we calculate the corresponding field strength (g), which is associated with the interpolating function (μ). In this way, a new relativistic potential is obtained (let us call 2nd Generalized Schwarzschild potential) which describes the gravitational interaction at any distance and for any metric of flat spacetime. Thus, not only the necessity for Dark Matter is eliminated, but also MOND becomes a pure Relativistic Theory of Gravitational Interaction. Then, we pass to the case of flat spacetime with Lorentz metric (Minkowski space), because the experimental data have been extracted using the Relativistic Doppler Shift and the gravitational red shift of Classic Relativity (CR). Thus, we Explain the Rotation Curves in Galaxies (e.g. NGC 3198) and Clusters of them as well as the Solar system, eliminating Dark Matter. This relativistic potential and the corresponding metric of spacetime have been obtained

Magnetized particle motion and acceleration around a Schwarzschild black hole in a magnetic field

International Nuclear Information System (INIS)

Abdujabbarov, Ahmadjon; Bobomurat Ahmedov; Rahimov, Ozodbek; Salikhbaev, Umar

2014-01-01

The capture cross section of magnetized particles with nonvanishing magnetic moment by a Schwarzschild black hole immersed in an asymptotically uniform magnetic field has been studied as an extension of the approach developed in Zakharov (1994 Class. Quantum Grav. 11 1027) for neutral unmagnetized particles in the Reissner–Nordström spacetime. The magnetic moment of the particle is chosen as in de Felice and Sorge (2003 Class. Quantum Grav. 20 469). It is shown that the spin of the particle sustains the stability of particles circularly orbiting around the black hole immersed in a magnetic field, i.e., a spinning particle's motion near the Schwarzschild black hole horizon is more stable than that of a particle with zero spin. It is shown that the magnetic parameter essentially changes the value of the critical angular momentum and affects the process of capture of the particles by the central black hole. Furthermore, the interaction between the magnetic moment of the particle and the magnetic field forces stable circular orbits to shift to the central object, and this effect should be taken into account in astrophysical scenarios related to the accretion discs and in measuring the spin of the black holes. The magnetized particle's acceleration mechanism near the black hole in an external magnetic field is studied. It is shown that due to the presence of a magnetic field, magnetized particles can accelerate to unlimited high energies. (paper)

Timelike geodesics around a charged spherically symmetric dilaton black hole

Directory of Open Access Journals (Sweden)

Blaga C.

2015-01-01

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

Continuous development of current sheets near and away from magnetic nulls

International Nuclear Information System (INIS)

Kumar, Sanjay; Bhattacharyya, R.

2016-01-01

The presented computations compare the strength of current sheets which develop near and away from the magnetic nulls. To ensure the spontaneous generation of current sheets, the computations are performed congruently with Parker's magnetostatic theorem. The simulations evince current sheets near two dimensional and three dimensional magnetic nulls as well as away from them. An important finding of this work is in the demonstration of comparative scaling of peak current density with numerical resolution, for these different types of current sheets. The results document current sheets near two dimensional magnetic nulls to have larger strength while exhibiting a stronger scaling than the current sheets close to three dimensional magnetic nulls or away from any magnetic null. The comparative scaling points to a scenario where the magnetic topology near a developing current sheet is important for energetics of the subsequent reconnection.

Null-plane quantization of fermions

International Nuclear Information System (INIS)

Mustaki, D.

1990-01-01

Massive Dirac fermions are canonically quantized on the null plane using the Dirac-Bergmann algorithm. The procedure is carried out in the framework of quantum electrodynamics as an illustration of a rigorous treatment of interacting fermion fields

An axisymmetric evolution code for the Einstein equations on hyperboloidal slices

International Nuclear Information System (INIS)

Rinne, Oliver

2010-01-01

We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the computational cost. The formulation is based on an earlier axisymmetric evolution scheme, adapted to time slices of constant mean curvature. Ideas from a previous study by Moncrief and the author are applied in order to regularize the formally singular evolution equations at future null infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime are obtained, including a gravitational perturbation. The Bondi news function is evaluated at future null infinity.

Towards the proof of the cosmic censorship hypothesis

Energy Technology Data Exchange (ETDEWEB)

Krolak, Andrzej

1986-05-01

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

Can an observer really catch up with light?

International Nuclear Information System (INIS)

Tian, Guihua; Zheng, Zhao

2003-01-01

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

Towards the proof of the cosmic censorship hypothesis

International Nuclear Information System (INIS)

Krolak, Andrzej

1986-01-01

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

Kinematics of relative motion of test particles in general relativity

International Nuclear Information System (INIS)

Bazanski, S.L.

1977-01-01

A detailed mathematical study of the concept of geodesic deviation in pseudo-riemannian geometry is presented. A generalization of this concept to geodesic deviations of a higher order is then introduced and the second geodesic deviation is investigated in some detail. A geometric interpretation of the set of generalized geodesic deviations is given and applied in general relativity to determine a covariant and local description (with a desired order of accuracy) of test motions which take place in a certain finite neighbourhood of a given world line of an observer. The proper time evolution of two other objects related to geodesic deviation is also discussed: the space separation vector and the telescopic vector. This last name is given here to a field of null vectors along observer's world line which always point towards the same adjacent world line. The telescopic equations allow to determine the evolution of the frequency shift of electromagnetic radiation sent from and received on neighbouring world lines. On the basis of these equations also certain relations have been derived which connect the frequencies or frequency shifts with the curvature of space-time

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

International Nuclear Information System (INIS)

Villanueva, J. R.; Olivares, Marco

2015-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-11-15

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

Detection of long nulls in PSR B1706-16, a pulsar with large timing irregularities

Science.gov (United States)

Naidu, Arun; Joshi, Bhal Chandra; Manoharan, P. K.; Krishnakumar, M. A.

2018-04-01

Single pulse observations, characterizing in detail, the nulling behaviour of PSR B1706-16 are being reported for the first time in this paper. Our regular long duration monitoring of this pulsar reveals long nulls of 2-5 h with an overall nulling fraction of 31 ± 2 per cent. The pulsar shows two distinct phases of emission. It is usually in an active phase, characterized by pulsations interspersed with shorter nulls, with a nulling fraction of about 15 per cent, but it also rarely switches to an inactive phase, consisting of long nulls. The nulls in this pulsar are concurrent between 326.5 and 610 MHz. Profile mode changes accompanied by changes in fluctuation properties are seen in this pulsar, which switches from mode A before a null to mode B after the null. The distribution of null durations in this pulsar is bimodal. With its occasional long nulls, PSR B1706-16 joins the small group of intermediate nullers, which lie between the classical nullers and the intermittent pulsars. Similar to other intermediate nullers, PSR B1706-16 shows high timing noise, which could be due to its rare long nulls if one assumes that the slowdown rate during such nulls is different from that during the bursts.

Euclidean null controllability of nonlinear infinite delay systems with ...

African Journals Online (AJOL)

Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...

Hawking Radiation Spectra for Scalar Fields by a Higher-Dimensional Schwarzschild-de-Sitter Black Hole

OpenAIRE

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...

A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5×S5

International Nuclear Information System (INIS)

Hanada, Masanori; Maltz, Jonathan

2017-01-01

Based on 4d N=4 SYM on ℝ 1 ×S 3 , a gauge theory description of a small black hole in AdS 5 ×S 5 is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields’ eigenvalues plays a crucial role in this description. By analyzing the microcanonical ensemble, the Hagedorn behavior of long strings at low energy is obtained. Modulo an assumption based on the AdS/CFT duality for a large black hole, the energy of the small ten-dimensional Schwarzschild black hole E∼1/(G 10,N T 7 ) is derived. A heuristic gauge theory argument supporting this assumption is also given. The same argument applied to the ABJM theory correctly reproduces the relation for the eleven-dimensional Schwarzschild black hole. One of the consequences of our proposal is that the small and large black holes are very similar when seen from the gauge theory point of view.

Visual and Plastic Arts in Teaching Literacy: Null Curricula?

Science.gov (United States)

Wakeland, Robin Gay

2010-01-01

Visual and plastic arts in contemporary literacy instruction equal null curricula. Studies show that painting and sculpture facilitate teaching reading and writing (literacy), yet such pedagogy has not been formally adopted into USA curriculum. An example of null curriculum can be found in late 19th - early 20th century education the USA…

Losses at magnetic nulls in pulsed-power transmission line systems

International Nuclear Information System (INIS)

Mendel, C.W. Jr.; Pointon, T.D.; Savage, M.E.; Seidel, D.B.; Magne, I.; Vezinet, R.

2006-01-01

Pulsed-power systems operating in the terawatt regime must deal with large electron flows in vacuum transmission lines. In most parts of these transmission lines the electrons are constrained by the self-magnetic field to flow parallel to the conductors. In very low impedance systems, such as those used to drive Z-pinch radiation sources, the currents from multiple transmission lines are added together. This addition necessarily involves magnetic nulls that connect the positive and negative electrodes. The resultant local loss of magnetic insulation results in electron losses at the anode in the vicinity of the nulls. The lost current due to the magnetic null might or might not be appreciable. In some cases the lost current due to the null is not large, but is spatially localized, and may create a gas and plasma release from the anode that can lead to an excessive loss, and possibly to catastrophic damage to the hardware. In this paper we describe an analytic model that uses one geometric parameter (aside from straightforward hardware size measurements) that determines the loss to the anode, and the extent of the loss region when the driving source and load are known. The parameter can be calculated in terms of the magnetic field in the region of the null calculated when no electron flow is present. The model is compared to some experimental data, and to simulations of several different hardware geometries, including some cases with multiple nulls, and unbalanced feeds

Current singularities at finitely compressible three-dimensional magnetic null points

International Nuclear Information System (INIS)

Pontin, D.I.; Craig, I.J.D.

2005-01-01

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed

Null but not void: considerations for hypothesis testing.

Science.gov (United States)

Shaw, Pamela A; Proschan, Michael A

2013-01-30

Standard statistical theory teaches us that once the null and alternative hypotheses have been defined for a parameter, the choice of the statistical test is clear. Standard theory does not teach us how to choose the null or alternative hypothesis appropriate to the scientific question of interest. Neither does it tell us that in some cases, depending on which alternatives are realistic, we may want to define our null hypothesis differently. Problems in statistical practice are frequently not as pristinely summarized as the classic theory in our textbooks. In this article, we present examples in statistical hypothesis testing in which seemingly simple choices are in fact rich with nuance that, when given full consideration, make the choice of the right hypothesis test much less straightforward. Published 2012. This article is a US Government work and is in the public domain in the USA.

High-contrast Nulling Interferometry Techniques Project

Data.gov (United States)

National Aeronautics and Space Administration — "We are developing rotating-baseline nulling-interferometry techniques and algorithms on the single-aperture Hale and Keck telescopes at near-infrared wavelengths,...

A model for electron currents near a field null

International Nuclear Information System (INIS)

Stark, R.A.; Miley, G.H.

1987-01-01

The fluid approximation is invalid near a field null, since the local electron orbit size and the magnetic scale length are comparable. To model the electron currents in this region we propose a single equation of motion describing the bulk electron dynamics. The equation applies to the plasma within one thermal orbit size of the null. The region is treated as unmagnetized; electrons are accelerated by the inductive electric field and drag on ions; damping is provided by viscosity due to electrons and collisions with ions. Through variational calculations and a particle tracking code for electrons, the size of the terms in the equation of motion have been estimated. The resulting equation of motion combines with Faraday's Law to produce a governing equation which implicitly contains the self inductive field of the electrons. This governing equation predicts that viscosity prevents complete cancellation of the ion current density by the electrons in the null region. Thus electron dynamics near the field null should not prevent the formation and deepening of field reversal using neutral-beam injection

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

Science.gov (United States)

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

2014-02-01

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

Regge calculus and observations. II. Further applications.

Science.gov (United States)

Williams, Ruth M.; Ellis, G. F. R.

1984-11-01

The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.

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

Directory of Open Access Journals (Sweden)

DanFang Yan

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

Stability analysis and quasinormal modes of Reissner–Nordstrøm ...

Indian Academy of Sciences (India)

2016-06-09

Jun 9, 2016 ... They also determine important features of the space-time and give important information on the background geometry. The Lyapunov exponent (λ) has been used to probe the instability of circular null geodesics and in terms of the quasinormal modes (QNMs) for spherically symmetric space-time of arbitrary ...

Entropy Measures as Geometrical Tools in the Study of Cosmology

Directory of Open Access Journals (Sweden)

Gilbert Weinstein

2017-12-01

Full Text Available Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x with χ ( x being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double-warped spacetime leads to the same entropy equation. By applying a Robertson–Walker metric for a flat three-dimensional Euclidean space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Riccati equation similar to the transformed entropy equation. Those Riccati-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of general relativity and cosmology. We suggest a refined entropy measure applicable in cosmology and defined by the average deviation of the geodesics in a congruence.

Large N phase transitions and the fate of small Schwarzschild-AdS black holes

Science.gov (United States)

Yaffe, Laurence G.

2018-01-01

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS5×S5 spacetime are known to become dynamically unstable toward deformation of the internal S5 geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-N Yang-Mills theory on R ×S3. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large-N limit in the dual field theory and typical large volume thermodynamic limits.

Kerr metric in the deSitter background

International Nuclear Information System (INIS)

Vaidya, P.C.

1984-01-01

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein's equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild's exterior metric with cosmological constant. (author)

Characteristics of transonic spherical symmetric accretion flow in Schwarzschild-de Sitter and Schwarzschild anti-de Sitter backgrounds, in pseudo-general relativistic paradigm

Science.gov (United States)

Ghosh, Shubhrangshu; Banik, Prabir

2015-07-01

In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central

Accretion of a symmetry-breaking scalar field by a Schwarzschild black hole.

Science.gov (United States)

Traykova, Dina; Braden, Jonathan; Peiris, Hiranya V

2018-03-06

We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry-breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory.This article is part of the Theo Murphy meeting issue 'Higgs Cosmology'. © 2018 The Author(s).

Comment on "Comments on `The Euclidean gravitational action as black hole entropy, singularities and space-time voids'" [J. Math. Phys. 50, 042502 (2009)]-Schwarzschild black hole lives to fight another day

Science.gov (United States)

Kundu, Prasun K.

2017-11-01

In a comment published several years ago in this journal, Mitra [J. Math. Phys. 50, 042502 (2009)] has claimed to prove that a neutral point particle in general relativity as described by the Schwarzschild metric must have zero gravitational mass, i.e., the mass parameter M0 of a Schwarzschild black hole necessarily vanishes. It is shown that the purported proof is incorrect. The error stems from a basic misunderstanding of the mathematical description of coordinate volume element in a differentiable manifold.

Sequential weak continuity of null Lagrangians at the boundary

Czech Academy of Sciences Publication Activity Database

Kalamajska, A.; Kraemer, S.; Kružík, Martin

2014-01-01

Roč. 49, 3/4 (2014), s. 1263-1278 ISSN 0944-2669 R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:67985556 Keywords : null Lagrangians * nonhomogeneous nonlinear mappings * sequential weak/in measure continuity Subject RIV: BA - General Mathematics Impact factor: 1.518, year: 2014 http://library.utia.cas.cz/separaty/2013/MTR/kruzik-sequential weak continuity of null lagrangians at the boundary.pdf

A parameter set for a double-null DEMO reactor

International Nuclear Information System (INIS)

Cooke, P.I.H.

1987-01-01

The present study is aimed at commenting on the reactor-relevance of the design principles and technology being proposed for NET. The authors propose that a double-null device serve as a basis for a NET-based demonstration reactor. Calculations are carried out to determine the parameter set for reactors based on the double-null NET design, and the results are presented in tabular form. (U.K.)

Quantum maps of geodesic flows on surfaces of constant negative curvature

International Nuclear Information System (INIS)

Bogomolny, E.B.; Carioli, M.

1992-01-01

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

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

Science.gov (United States)

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

2017-07-01

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

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

Science.gov (United States)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-09-01

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

sirt1-null mice develop an autoimmune-like condition

International Nuclear Information System (INIS)

Sequeira, Jedon; Boily, Gino; Bazinet, Stephanie; Saliba, Sarah; He Xiaohong; Jardine, Karen; Kennedy, Christopher; Staines, William; Rousseaux, Colin; Mueller, Rudi; McBurney, Michael W.

2008-01-01

The sirt1 gene encodes a protein deacetylase with a broad spectrum of reported substrates. Mice carrying null alleles for sirt1 are viable on outbred genetic backgrounds so we have examined them in detail to identify the biological processes that are dependent on SIRT1. Sera from adult sirt1-null mice contain antibodies that react with nuclear antigens and immune complexes become deposited in the livers and kidneys of these animals. Some of the sirt1-null animals develop a disease resembling diabetes insipidus when they approach 2 years of age although the relationship to the autoimmunity remains unclear. We interpret these observations as consistent with a role for SIRT1 in sustaining normal immune function and in this way delaying the onset of autoimmune disease

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

Czech Academy of Sciences Publication Activity Database

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

2017-01-01

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

Dynamics of stringy congruence in the early universe

International Nuclear Information System (INIS)

Cho, Yong Seung; Hong, Soon-Tae

2011-01-01

We study twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the twist and shear in terms of the expansion of the Universe. We observe in this higher dimensional cosmology that, as the early universe evolves with expansion rate, the twist of the stringy congruence decreases exponentially and the initial twist value should be large enough to sustain the rotations of the ensuing universe, while the effects of the shear are negligible to produce the isotropic and homogeneous universe. We also investigate the twist and shear of the geodesic surface congruence of the null strings.

Probing quantum entanglement in the Schwarzschild space-time beyond the single-mode approximation

Science.gov (United States)

He, Juan; Ding, Zhi-Yong; Ye, Liu

2018-05-01

In this paper, we deduce the vacuum structure for Dirac fields in the background of Schwarzschild space-time beyond the single-mode approximation and discuss the performance of quantum entanglement between particle and antiparticle modes of a Dirac field with Hawking effect. It is shown that Hawking radiation does not always destroy the physically accessible entanglement, and entanglement amplification may happen in some cases. This striking result is different from that of the single-mode approximation, which holds that the Hawking radiation can only destroy entanglement. Lastly, we analyze the physically accessible entanglement relation outside the event horizon and demonstrate that the monogamy inequality is constantly established regardless of the choice of given parameters.

Null point of discrimination in crustacean polarisation vision.

Science.gov (United States)

How, Martin J; Christy, John; Roberts, Nicholas W; Marshall, N Justin

2014-07-15

The polarisation of light is used by many species of cephalopods and crustaceans to discriminate objects or to communicate. Most visual systems with this ability, such as that of the fiddler crab, include receptors with photopigments that are oriented horizontally and vertically relative to the outside world. Photoreceptors in such an orthogonal array are maximally sensitive to polarised light with the same fixed e-vector orientation. Using opponent neural connections, this two-channel system may produce a single value of polarisation contrast and, consequently, it may suffer from null points of discrimination. Stomatopod crustaceans use a different system for polarisation vision, comprising at least four types of polarisation-sensitive photoreceptor arranged at 0, 45, 90 and 135 deg relative to each other, in conjunction with extensive rotational eye movements. This anatomical arrangement should not suffer from equivalent null points of discrimination. To test whether these two systems were vulnerable to null points, we presented the fiddler crab Uca heteropleura and the stomatopod Haptosquilla trispinosa with polarised looming stimuli on a modified LCD monitor. The fiddler crab was less sensitive to differences in the degree of polarised light when the e-vector was at -45 deg than when the e-vector was horizontal. In comparison, stomatopods showed no difference in sensitivity between the two stimulus types. The results suggest that fiddler crabs suffer from a null point of sensitivity, while stomatopods do not. © 2014. Published by The Company of Biologists Ltd.

Logarithmic corrections to gravitational entropy and the null energy condition

Energy Technology Data Exchange (ETDEWEB)

Parikh, Maulik, E-mail: maulik.parikh@asu.edu; Svesko, Andrew

2016-10-10

Using a relation between the thermodynamics of local horizons and the null energy condition, we consider the effects of quantum corrections to the gravitational entropy. In particular, we find that the geometric form of the null energy condition is not affected by the inclusion of logarithmic corrections to the Bekenstein–Hawking entropy.

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-11-15

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

Yang-Mills theory in null path space

International Nuclear Information System (INIS)

Kent, S.L.

1982-01-01

A reformulation of classical GL(n,c) Yang-Mills theory is presented. The reformulation is in terms of a single matrix-valued function G on a six-dimensional subspace of the space of paths in Minkowski space, M. This subspace is defined as the null paths beginning at each point, (X/sup a/), of M and ending at future null infinity. A convenient parametrization of these paths is to give the Minkowski coordinates x/sup a/ of the starting point and the (complex) stereographic coordinates (xi, antixi) on S 2 which label the light cone generators of x/sup a/. A path is thus labeled by (x/sup a/,xi, antixi). The function G(x/sup a/,xi, antixi) is defined by the parallel propagation (with a given connection) of n linearly independent fiber vectors from x/sup a/ to null infinity along the (xi, antixi) generator. From knowledge of G(x/sup a/,xi, antixi) the connection one-form γ/sub a/ at the point x/sup a/ can be obtained is shown. Furthermore how the vacuum Yang-Mills equations can be imposed on the G is shown. This results in a rather complicated integro-differential equation for G which involves the characteristic initial data (essentially the radiation field) acting as the driving term. Two simple special cases are immediately obtainable; in the case of self-dual (or anti-self dual) fields the author obtains a simple derivation of the Sparling equation, namely delta G = -GA, while for Abelian (Maxwell) theories obtained the equation delta anti delta log G = -anti delta A-anti delta A, where A and its conjugate anti A are the characteristic free data given on null infinity. The latter equation is equivalent to the vacuum Maxwell equations

Logarithmic corrections to gravitational entropy and the null energy condition

Directory of Open Access Journals (Sweden)

Maulik Parikh

2016-10-01

Full Text Available Using a relation between the thermodynamics of local horizons and the null energy condition, we consider the effects of quantum corrections to the gravitational entropy. In particular, we find that the geometric form of the null energy condition is not affected by the inclusion of logarithmic corrections to the Bekenstein–Hawking entropy.

The data-driven null models for information dissemination tree in social networks

Science.gov (United States)

Zhang, Zhiwei; Wang, Zhenyu

2017-10-01

For the purpose of detecting relatedness and co-occurrence between users, as well as the distribution features of nodes in spreading path of a social network, this paper explores topological characteristics of information dissemination trees (IDT) that can be employed indirectly to probe the information dissemination laws within social networks. Hence, three different null models of IDT are presented in this article, including the statistical-constrained 0-order IDT null model, the random-rewire-broken-edge 0-order IDT null model and the random-rewire-broken-edge 2-order IDT null model. These null models firstly generate the corresponding randomized copy of an actual IDT; then the extended significance profile, which is developed by adding the cascade ratio of information dissemination path, is exploited not only to evaluate degree correlation of two nodes associated with an edge, but also to assess the cascade ratio of different length of information dissemination paths. The experimental correspondences of the empirical analysis for several SinaWeibo IDTs and Twitter IDTs indicate that the IDT null models presented in this paper perform well in terms of degree correlation of nodes and dissemination path cascade ratio, which can be better to reveal the features of information dissemination and to fit the situation of real social networks.

Circuital model for the spherical geodesic waveguide perfect drain

Science.gov (United States)

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

2012-08-01

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

Circuital model for the spherical geodesic waveguide perfect drain

International Nuclear Information System (INIS)

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

2012-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-06-01

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

Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua

International Nuclear Information System (INIS)

Figueras, Pau; Lucietti, James; Wiseman, Toby

2011-01-01

The elliptic Einstein-DeTurck equation may be used to numerically find Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics are considered by analytically continuing to Euclidean time. The Ricci-DeTurck flow is a constructive algorithm to solve this equation, and is simple to implement when the solution is a stable fixed point, the only complication being that Ricci solitons may exist which are not Einstein. Here we extend previous work to consider the Einstein-DeTurck equation for Riemannian manifolds with boundaries, and those that continue to static Lorentzian spacetimes which are asymptotically flat, Kaluza-Klein, locally AdS or have extremal horizons. Using a maximum principle, we prove that Ricci solitons do not exist in these cases and so any solution is Einstein. We also argue that the Ricci-DeTurck flow preserves these classes of manifolds. As an example, we simulate the Ricci-DeTurck flow for a manifold with asymptotics relevant for AdS 5 /CFT 4 . Our maximum principle dictates that there are no soliton solutions, and we give strong numerical evidence that there exists a stable fixed point of the flow which continues to a smooth static Lorentzian Einstein metric. Our asymptotics are such that this describes the classical gravity dual relevant for the CFT on a Schwarzschild background in either the Unruh or Boulware vacua. It determines the leading O(N 2 c ) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons. (paper)

Motions in the relativistic fields of a charged dust

International Nuclear Information System (INIS)

Fonseca Teixeira, A.F. da.

1980-04-01

The general relativistic motion of arbitrarily charged test particles is investigated, in the spherically symmetric fields of a charged, static, incoherent matter with T 0 0 = const. The condition for existence of stable circular orbits is established, inside and outside the diffused source. The null geodesics are also investigated, as a limiting case. (Author) [pt

Integrability and black-hole microstate geometries

Science.gov (United States)

Bena, Iosif; Turton, David; Walker, Robert; Warner, Nicholas P.

2017-11-01

We examine some recently-constructed families of asymptotically-AdS3 × S^3 supergravity solutions that have the same charges and mass as supersymmetric D1-D5- P black holes, but that cap off smoothly with no horizon. These solutions, known as superstrata, are quite complicated, however we show that, for an infinite family of solutions, the null geodesic problem is completely integrable, due to the existence of a non-trivial conformal Killing tensor that provides a quadratic conservation law for null geodesics. This implies that the massless scalar wave equation is separable. For another infinite family of solutions, we find that there is a non-trivial conformal Killing tensor only when the left-moving angular momentum of the massless scalar is zero. We also show that, for both these families, the metric degrees of freedom have the form they would take if they arose from a consistent truncation on S^3 down to a (2 + 1)-dimensional space-time. We discuss some of the broader consequences of these special properties for the physics of these black-hole microstate geometries.

On the geometry of null congruences in general relativity

International Nuclear Information System (INIS)

Ahsan, Zafar; Malik, N.P.

1977-01-01

Some theorems for the null congruences within the framework of general theory of relativity are given. These theorems are important in themselves as they illustrate the geometric meaning of the spin coefficients. The newly developed Geroch-Held-Penrose (GHP) formalism has been used throughout the investigations. The salient features of GHP formalism that are necessary for the present work are given and these techniques are applied to a pair of null congruences C(l) and C(n). (author)

Dirac equation for massive neutrinos in a Schwarzschild-de Sitter spacetime from a 5D vacuum

International Nuclear Information System (INIS)

Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

2011-01-01

Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.

pyNSMC: A Python Module for Null-Space Monte Carlo Uncertainty Analysis

Science.gov (United States)

White, J.; Brakefield, L. K.

2015-12-01

The null-space monte carlo technique is a non-linear uncertainty analyses technique that is well-suited to high-dimensional inverse problems. While the technique is powerful, the existing workflow for completing null-space monte carlo is cumbersome, requiring the use of multiple commandline utilities, several sets of intermediate files and even a text editor. pyNSMC is an open-source python module that automates the workflow of null-space monte carlo uncertainty analyses. The module is fully compatible with the PEST and PEST++ software suites and leverages existing functionality of pyEMU, a python framework for linear-based uncertainty analyses. pyNSMC greatly simplifies the existing workflow for null-space monte carlo by taking advantage of object oriented design facilities in python. The core of pyNSMC is the ensemble class, which draws and stores realized random vectors and also provides functionality for exporting and visualizing results. By relieving users of the tedium associated with file handling and command line utility execution, pyNSMC instead focuses the user on the important steps and assumptions of null-space monte carlo analysis. Furthermore, pyNSMC facilitates learning through flow charts and results visualization, which are available at many points in the algorithm. The ease-of-use of the pyNSMC workflow is compared to the existing workflow for null-space monte carlo for a synthetic groundwater model with hundreds of estimable parameters.

Fabrication of nanoscale patterns in lithium fluoride crystal using a 13.5 nm Schwarzschild objective and a laser produced plasma source

International Nuclear Information System (INIS)

Wang Xin; Mu Baozhong; Jiang Li; Zhu Jingtao; Yi Shengzhen; Wang Zhanshan; He Pengfei

2011-01-01

Lithium fluoride (LiF) crystal is a radiation sensitive material widely used as EUV and soft x-ray detector. The LiF-based detector has high resolution, in principle limited by the point defect size, large field of view, and wide dynamic range. Using LiF crystal as an imaging detector, a resolution of 900 nm was achieved by a projection imaging of test meshes with a Schwarzschild objective operating at 13.5 nm. In addition, by imaging of a pinhole illuminated by the plasma, an EUV spot of 1.5 μm diameter in the image plane of the objective was generated, which accomplished direct writing of color centers with resolution of 800 nm. In order to avoid sample damage and contamination due to the influence of huge debris flux produced by the plasma source, a spherical normal-incidence condenser was used to collect EUV radiation. Together with a description of experimental results, the development of the Schwarzschild objective, the influence of condenser on energy density and the alignment of the imaging system are also reported.

Spectroscopy of the Schwarzschild black hole at arbitrary frequencies.

Science.gov (United States)

Casals, Marc; Ottewill, Adrian

2012-09-14

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.

Testing the null hypothesis: the forgotten legacy of Karl Popper?

Science.gov (United States)

Wilkinson, Mick

2013-01-01

Testing of the null hypothesis is a fundamental aspect of the scientific method and has its basis in the falsification theory of Karl Popper. Null hypothesis testing makes use of deductive reasoning to ensure that the truth of conclusions is irrefutable. In contrast, attempting to demonstrate the new facts on the basis of testing the experimental or research hypothesis makes use of inductive reasoning and is prone to the problem of the Uniformity of Nature assumption described by David Hume in the eighteenth century. Despite this issue and the well documented solution provided by Popper's falsification theory, the majority of publications are still written such that they suggest the research hypothesis is being tested. This is contrary to accepted scientific convention and possibly highlights a poor understanding of the application of conventional significance-based data analysis approaches. Our work should remain driven by conjecture and attempted falsification such that it is always the null hypothesis that is tested. The write up of our studies should make it clear that we are indeed testing the null hypothesis and conforming to the established and accepted philosophical conventions of the scientific method.

Null controllability of a cascade system of Schrodinger equations

Directory of Open Access Journals (Sweden)

Marcos Lopez-Garcia

2016-03-01

Full Text Available This article presents a control problem for a cascade system of two linear N-dimensional Schrodinger equations. We address the problem of null controllability by means of a control supported in a region not satisfying the classical geometrical control condition. The proof is based on the application of a Carleman estimate with degenerate weights to each one of the equations and a careful analysis of the system in order to prove null controllability with only one control force.

Extreme super-resolution using the spherical geodesic waveguide

Science.gov (United States)

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

2012-06-01

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

Do static atoms outside a Schwarzschild black hole spontaneously excite?

International Nuclear Information System (INIS)

Yu Hongwei; Zhou Wenting

2007-01-01

The spontaneous excitation of a two-level atom held static outside a four dimensional Schwarzschild black hole and in interaction with a massless scalar field in the Boulware, Unruh, and Hartle-Hawking vacuums is investigated, and the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy are calculated separately. We find that, for the Boulware vacuum, the spontaneous excitation does not occur and the ground-state atoms are stable, while the spontaneous emission rate for excited atoms in the Boulware vacuum, which is well behaved at the event horizon, is not the same as that in the usual Minkowski vacuum. However, for both the Unruh vacuum and the Hartle-Hawking vacuum, our results show that the atom would spontaneously excite, as if there were an outgoing thermal flux of radiation or as if it were in a thermal bath of radiation at a proper temperature which reduces to the Hawking temperature in the spatial asymptotic region, depending on whether the scalar field is in the Unruh or Hartle-Hawking vacuum

THE NATURE OF FLARE RIBBONS IN CORONAL NULL-POINT TOPOLOGY

International Nuclear Information System (INIS)

Masson, S.; Aulanier, G.; Pariat, E.; Schrijver, C. J.

2009-01-01

Flare ribbons are commonly attributed to the low-altitude impact, along the footprints of separatrices or quasi-separatrix layers (QSLs), of particle beams accelerated through magnetic reconnection. If reconnection occurs at a three-dimensional coronal magnetic null point, the footprint of the dome-shaped fan surface would map a closed circular ribbon. This paper addresses the following issues: does the entire circular ribbon brighten simultaneously, as expected because all fan field lines pass through the null point? And since the spine separatrices are singular field lines, do spine-related ribbons look like compact kernels? What can we learn from these observations about current sheet formation and magnetic reconnection in a null-point topology? The present study addresses these questions by analyzing Transition Region and Coronal Explorer and Solar and Heliospheric Observatory/Michelson Doppler Imager observations of a confined flare presenting a circular ribbon. Using a potential field extrapolation, we linked the circular shape of the ribbon with the photospheric mapping of the fan field lines originating from a coronal null point. Observations show that the flare ribbon outlining the fan lines brightens sequentially along the counterclockwise direction and that the spine-related ribbons are elongated. Using the potential field extrapolation as initial condition, we conduct a low-β resistive magnetohydrodynamics simulation of this observed event. We drive the coronal evolution by line-tied diverging boundary motions, so as to emulate the observed photospheric flow pattern associated with some magnetic flux emergence. The numerical analysis allows us to explain several observed features of the confined flare. The vorticity induced in the fan by the prescribed motions causes the spines to tear apart along the fan. This leads to formation of a thin current sheet and induces null-point reconnection. We also find that the null point and its associated topological

The (2, 0) superalgebra, null M-branes and Hitchin's system

Science.gov (United States)

Kucharski, P.; Lambert, N.; Owen, M.

2017-10-01

We present an interacting system of equations with sixteen supersymmetries and an SO(2) × SO(6) R-symmetry where the fields depend on two space and one null dimensions that is derived from a representation of the six-dimensional (2, 0) superalgebra. The system can be viewed as two M5-branes compactified on {S}-^1× T^2 or equivalently as M2-branes on R+× R^2 , where ± refer to null directions. We show that for a particular choice of fields the dynamics can be reduced to motion on the moduli space of solutions to the Hitchin system. We argue that this provides a description of intersecting null M2-branes and is also related by U-duality to a DLCQ description of four-dimensional maximally supersymmetric Yang-Mills.

Vacuum Nuller Testbed (VNT) Performance, Characterization and Null Control: Progress Report

Science.gov (United States)

Lyon, Richard G.; Clampin, Mark; Petrone, Peter; Mallik, Udayan; Madison, Timothy; Bolcar, Matthew R.; Noecker, M. Charley; Kendrick, Stephen; Helmbrecht, Michael

2011-01-01

Herein we report on the development. sensing and control and our first results with the Vacuum Nuller Testbed to realize a Visible Nulling Coronagraph (VNC) for exoplanet coronagraphy. The VNC is one of the few approaches that works with filled. segmented and sparse or diluted-aperture telescope systems. It thus spans a range of potential future NASA telescopes and could be Hown as a separate instrument on such a future mission. NASA/Goddard Space Flight Center (GSFC) has a well-established effort to develop VNC technologies. and has developed an incremental sequence of VNC testbeds to advance this approach and the enabling technologies associated with it. We discuss the continued development of the vacuum Visible Nulling Coronagraph testbed (VNT). Tbe VNT is an ultra-stable vibration isolated testbed that operates under closed-loop control within a vacuum chamber. It will be used to achieve an incremental sequence of three visible-light nulling milestones with sequentially higher contrasts of 10(sup 8), 10(sup 9) and ideally 10(sup 10) at an inner working angle of 2*lambda/D. The VNT is based on a modified Mach-Zehnder nulling interferometer, with a "W" configuration to accommodate a hex-packed MEMS based deformable mirror, a coherent fiber bundle and achromatic phase shifters. We discuss the initial laboratory results, the optical configuration, critical technologies and the null sensing and control approach.

Vacuum nuller testbed (VNT) performance, characterization and null control: progress report

Science.gov (United States)

Lyon, Richard G.; Clampin, Mark; Petrone, Peter; Mallik, Udayan; Madison, Timothy; Bolcar, Matthew R.; Noecker, M. Charley; Kendrick, Stephen; Helmbrecht, Michael

2011-10-01

Herein we report on the development, sensing and control and our first results with the Vacuum Nuller Testbed to realize a Visible Nulling Coronagraph (VNC) for exoplanet coronagraphy. The VNC is one of the few approaches that works with filled, segmented and sparse or diluted-aperture telescope systems. It thus spans a range of potential future NASA telescopes and could be flown as a separate instrument on such a future mission. NASA/Goddard Space Flight Center (GSFC) has a well-established effort to develop VNC technologies, and has developed an incremental sequence of VNC testbeds to advance this approach and the enabling technologies associated with it. We discuss the continued development of the vacuum Visible Nulling Coronagraph testbed (VNT). The VNT is an ultra-stable vibration isolated testbed that operates under closed-loop control within a vacuum chamber. It will be used to achieve an incremental sequence of three visible-light nulling milestones with sequentially higher contrasts of 108, 109, and ideally 1010 at an inner working angle of 2*λ/D. The VNT is based on a modified Mach-Zehnder nulling interferometer, with a "W" configuration to accommodate a hex-packed MEMS based deformable mirror, a coherent fiber bundle and achromatic phase shifters. We discuss the initial laboratory results, the optical configuration, critical technologies and the null sensing and control approach.

Nulling tomography with weak gravitational lensing

International Nuclear Information System (INIS)

Huterer, Dragan; White, Martin

2005-01-01

We explore several strategies of eliminating (or nulling) the small-scale information in weak lensing convergence power spectrum measurements in order to protect against undesirable effects, for example, the effects of baryonic cooling and pressure forces on the distribution of large-scale structures. We selectively throw out the small-scale information in the convergence power spectrum that is most sensitive to the unwanted bias, while trying to retain most of the sensitivity to cosmological parameters. The strategies are effective in the difficult but realistic situations when we are able to guess the form of the contaminating effect only approximately. However, we also find that the simplest scheme of simply not using information from the largest multipoles works about as well as the proposed techniques in most, although not all, realistic cases. We advocate further exploration of nulling techniques and believe that they will find important applications in the weak lensing data mining

A generalized sine condition and performance comparison of Wolter type II and Wolter-Schwarzschild extreme ultraviolet telescopes

Science.gov (United States)

Saha, T. T.

1984-01-01

An equation similar to the Abbe sine condition is derived for a Wolter type II telescope. This equation and the sine condition are then combined to produce a so called generalized sine condition. Using the law of reflection, Fermat's principle, the generalized sine condition, and simple geometry the surface equations for a Wolter type II telescope and an equivalent Wolter-Schwarzschild telescope are calculated. The performances of the telescopes are compared in terms of rms blur circle radius at the Gaussian focal plane and at best focus.

An improved null model for assessing the net effects of multiple stressors on communities.

Science.gov (United States)

Thompson, Patrick L; MacLennan, Megan M; Vinebrooke, Rolf D

2018-01-01

Ecological stressors (i.e., environmental factors outside their normal range of variation) can mediate each other through their interactions, leading to unexpected combined effects on communities. Determining whether the net effect of stressors is ecologically surprising requires comparing their cumulative impact to a null model that represents the linear combination of their individual effects (i.e., an additive expectation). However, we show that standard additive and multiplicative null models that base their predictions on the effects of single stressors on community properties (e.g., species richness or biomass) do not provide this linear expectation, leading to incorrect interpretations of antagonistic and synergistic responses by communities. We present an alternative, the compositional null model, which instead bases its predictions on the effects of stressors on individual species, and then aggregates them to the community level. Simulations demonstrate the improved ability of the compositional null model to accurately provide a linear expectation of the net effect of stressors. We simulate the response of communities to paired stressors that affect species in a purely additive fashion and compare the relative abilities of the compositional null model and two standard community property null models (additive and multiplicative) to predict these linear changes in species richness and community biomass across different combinations (both positive, negative, or opposite) and intensities of stressors. The compositional model predicts the linear effects of multiple stressors under almost all scenarios, allowing for proper classification of net effects, whereas the standard null models do not. Our findings suggest that current estimates of the prevalence of ecological surprises on communities based on community property null models are unreliable, and should be improved by integrating the responses of individual species to the community level as does our

Twistor quantisation of open strings in three dimensions

International Nuclear Information System (INIS)

Shaw, W.T.

1987-01-01

The paper treats the first quantisation of loops in real four-dimensional twistor space. Such loops correspond to open strings in three-dimensional spacetime. The geometry and reality structures pertaining to twistors in three dimensions are reviewed and the twistor description of null geodesics is presented as a prototype for the discussion of null curves. The classical twistor structure of null curves is then described. The symplectic structure is exhibited and used to investigate the constraint algebra. Expressions for the momentum operators are found. The symplectic structure defines natural canonical variables for covariant twistor quantisation and the consequences of carrying this out are described. A twistor representation of the Virasoro algebra with central charge 2 is found and some solutions of the quantum constraints are exhibited. (author)

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

Directory of Open Access Journals (Sweden)

V. I. Mikhailov

2010-01-01

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

Visible Nulling Coronagraphy for Exo-Planetary Detection and Characterization

Science.gov (United States)

Lyon, Richard G.; Clampin, Mark; Woodruff, Robert; Vasudevan, Gopal; Shao, Mike; Levine, Martin; Melnick, Gary; Tolls, Volker; Petrone, Peter; Dogoda, Peter; Duval, Julia; Ge, Jian

Visible Nulling Coronagraphy (VNC) is the proposed method of detecting and characterizing exo-solar Jovian planets (null depth 10-9) for the proposed NASA's Extrasolar Planetary Imaging Coronagraph (EPIC) Clampin & Lyon 2004 and is an approach under evaluation for NASA's Terrestrial Planet Finder (TPF) mission. The VNC approach uses a single unobscured filled-aperture telescope and splits, via a 50:50 beamsplitter, its re-imaged pupil into two paths within a Mach-Zender interferometer. An achromatic PI phase shift is imposed onto one beam path and the two paths are laterally sheared with respect to each other. The two beams are recombined at a second 50:50 beamsplitter. The net effect is that the on axis (stellar) light is transmitted out of the bright interferometer arm while the off-axis (planetary) light is transmitted out of the nulled interferometer arm. The bright output is used for fine pointing control and coarse wavefront control. The nulled output is relayed to the science camera for science imagery and fine wavefront control. The actual transmission pattern, projected on the sky, follows a θ^2 pattern for a single shear, θ^4 for a double shear, with the spacing of the successive maxima proportional to the inverse of the relative lateral shear. Combinations of shears and spacecraft rolls build up the spatial frequency content of the sky transmission pattern in the same manner as imaging interferometer builds up the spatial frequency content of the image.

Self-Nulling Beam Combiner Using No External Phase Inverter

Science.gov (United States)

Bloemhof, Eric E.

2010-01-01

A self-nulling beam combiner is proposed that completely eliminates the phase inversion subsystem from the nulling interferometer, and instead uses the intrinsic phase shifts in the beam splitters. Simplifying the flight instrument in this way will be a valuable enhancement of mission reliability. The tighter tolerances on R = T (R being reflection and T being transmission coefficients) required by the self-nulling configuration actually impose no new constraints on the architecture, as two adaptive nullers must be situated between beam splitters to correct small errors in the coatings. The new feature is exploiting the natural phase shifts in beam combiners to achieve the 180 phase inversion necessary for nulling. The advantage over prior art is that an entire subsystem, the field-flipping optics, can be eliminated. For ultimate simplicity in the flight instrument, one might fabricate coatings to very high tolerances and dispense with the adaptive nullers altogether, with all their moving parts, along with the field flipper subsystem. A single adaptive nuller upstream of the beam combiner may be required to correct beam train errors (systematic noise), but in some circumstances phase chopping reduces these errors substantially, and there may be ways to further reduce the chop residuals. Though such coatings are beyond the current state of the art, the mechanical simplicity and robustness of a flight system without field flipper or adaptive nullers would perhaps justify considerable effort on coating fabrication.

Null cone superspace supergravity

International Nuclear Information System (INIS)

Downes-Martin, S.G.

1980-03-01

The null cone formalism is used to derive a 2(N-1) parameter family of constraints for O(N) extended superspace supergravity. The invariance groups of these constraints is analysed and is found to be [subgroup U submanifold] contains GL(4,R) for N = 1, the submanifold being eliminated for N > 1. The invariance group defines non-Weyl rotations on the superbein which combine to form Weyl transformations on the supertangent space metric. The invariance of the supergravity Lagrangian under these transformations is discussed. (Auth.)

High Contrast Vacuum Nuller Testbed (VNT) Contrast, Performance and Null Control

Science.gov (United States)

Lyon, Richard G.; Clampin, Mark; Petrone, Peter; Mallik, Udayan; Madison, Timothy; Bolcar, Matthew R.

2012-01-01

Herein we report on our Visible Nulling Coronagraph high-contrast result of 109 contrast averaged over a focal planeregion extending from 14 D with the Vacuum Nuller Testbed (VNT) in a vibration isolated vacuum chamber. TheVNC is a hybrid interferometriccoronagraphic approach for exoplanet science. It operates with high Lyot stopefficiency for filled, segmented and sparse or diluted-aperture telescopes, thereby spanning the range of potential futureNASA flight telescopes. NASAGoddard Space Flight Center (GSFC) has a well-established effort to develop the VNCand its technologies, and has developed an incremental sequence of VNC testbeds to advance this approach and itsenabling technologies. These testbeds have enabled advancement of high-contrast, visible light, nulling interferometry tounprecedented levels. The VNC is based on a modified Mach-Zehnder nulling interferometer, with a W configurationto accommodate a hex-packed MEMS based deformable mirror, a coherent fiber bundle and achromatic phase shifters.We give an overview of the VNT and discuss the high-contrast laboratory results, the optical configuration, criticaltechnologies and null sensing and control.

High contrast vacuum nuller testbed (VNT) contrast, performance, and null control

Science.gov (United States)

Lyon, Richard G.; Clampin, Mark; Petrone, Peter; Mallik, Udayan; Madison, Timothy; Bolcar, Matthew R.

2012-09-01

Herein we report on our Visible Nulling Coronagraph high-contrast result of 109 contrast averaged over a focal plane region extending from 1 - 4 λ/D with the Vacuum Nuller Testbed (VNT) in a vibration isolated vacuum chamber. The VNC is a hybrid interferometric/coronagraphic approach for exoplanet science. It operates with high Lyot stop efficiency for filled, segmented and sparse or diluted-aperture telescopes, thereby spanning the range of potential future NASA flight telescopes. NASA/Goddard Space Flight Center (GSFC) has a well-established effort to develop the VNC and its technologies, and has developed an incremental sequence of VNC testbeds to advance this approach and its enabling technologies. These testbeds have enabled advancement of high-contrast, visible light, nulling interferometry to unprecedented levels. The VNC is based on a modified Mach-Zehnder nulling interferometer, with a “W” configuration to accommodate a hex-packed MEMS based deformable mirror, a coherent fiber bundle and achromatic phase shifters. We give an overview of the VNT and discuss the high-contrast laboratory results, the optical configuration, critical technologies and null sensing and control.

Spatial and null infinity via advanced and retarded conformal factors

International Nuclear Information System (INIS)

Hayward, Sean A.

2003-01-01

A new approach to space-time asymptotics is presented, refining Penrose's idea of conformal transformations with infinity represented by the conformal boundary of space-time. It is proposed that the Penrose conformal factor be a product of advanced and retarded conformal factors, which asymptotically relate physical and conformal null coordinates and vanish at future and past null infinity respectively. A refined definition of asymptotic flatness at both spatial and null infinity is given, including that the conformal boundary is locally a light cone, with spatial infinity as the vertex. It is shown how to choose the conformal factors so that this asymptotic light cone is locally a metric light cone. The theory is implemented in the spin-coefficient (or null-tetrad) formalism by a joint transformation of the spin-metric and spin-basis (or metric and tetrad). Asymptotic regularity conditions are proposed, based on the conformal boundary locally being a smoothly embedded metric light cone. These conditions ensure that the Bondi-Sachs energy-flux integrals of ingoing and outgoing gravitational radiation decay at spatial infinity such that the total radiated energy is finite, and that the Bondi-Sachs energy-momentum has a unique limit at spatial infinity, coinciding with the uniquely rendered ADM energy-momentum

Unicorns do exist: a tutorial on "proving" the null hypothesis.

Science.gov (United States)

Streiner, David L

2003-12-01

Introductory statistics classes teach us that we can never prove the null hypothesis; all we can do is reject or fail to reject it. However, there are times when it is necessary to try to prove the nonexistence of a difference between groups. This most often happens within the context of comparing a new treatment against an established one and showing that the new intervention is not inferior to the standard. This article first outlines the logic of "noninferiority" testing by differentiating between the null hypothesis (that which we are trying to nullify) and the "nill" hypothesis (there is no difference), reversing the role of the null and alternate hypotheses, and defining an interval within which groups are said to be equivalent. We then work through an example and show how to calculate sample sizes for noninferiority studies.

Causal null hypotheses of sustained treatment strategies: What can be tested with an instrumental variable?

Science.gov (United States)

Swanson, Sonja A; Labrecque, Jeremy; Hernán, Miguel A

2018-05-02

Sometimes instrumental variable methods are used to test whether a causal effect is null rather than to estimate the magnitude of a causal effect. However, when instrumental variable methods are applied to time-varying exposures, as in many Mendelian randomization studies, it is unclear what causal null hypothesis is tested. Here, we consider different versions of causal null hypotheses for time-varying exposures, show that the instrumental variable conditions alone are insufficient to test some of them, and describe additional assumptions that can be made to test a wider range of causal null hypotheses, including both sharp and average causal null hypotheses. Implications for interpretation and reporting of instrumental variable results are discussed.

Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VON)

Science.gov (United States)

Kulawiec, Andrew; Murphy, Paul; DeMarco, Michael

2010-10-01

Aspheric surfaces are proven to provide significant benefits to a wide variety of optical systems, but the ability to produce high-precision aspheric surfaces has historically been limited by the ability (or lack thereof) to measure them. Traditionally, aspheric measurements have required dedicated null optics, but the cost, lead time, and calibration difficulty of using null optics has made the use of aspheres more challenging and less attractive. In the past three years, QED has developed the Subaperture Stitching Interferometer for Aspheres (SSI-A®) to help address this limitation, providing flexible aspheric measurement capability of up to 200 waves of aspheric departure from best-fit sphere. Some aspheres, however, have thousands of waves of departure. We have recently developed Variable Optical Null (VON) technology that can null much of the aspheric departure in a subaperture. The VON is automatically configurable and is adjusted to nearly null each specific subaperture of an asphere. This ability to nearly null a local subaperture of an asphere provides a significant boost in aspheric measurement capability, enabling aspheres with up to 1000 waves of departure to be measured, without the use of dedicated null optics. We outline the basic principles of subaperture stitching and VON technology, demonstrate the extended capability provided by the VON, and present measurement results from the new Aspheric Stitching Interferometer (ASI®).

Broadband Active Segmented Aperture and Radial Shear Nulling

Data.gov (United States)

National Aeronautics and Space Administration — The Visible Nulling Coronagraph (VNC) is a starlight suppression system for enabling exoplanet detectionand atmospheric measurement. Conceptual space telescope...

Null canonical formalism 1, Maxwell field. [Poisson brackets, boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Wodkiewicz, K [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej

1975-01-01

The purpose of this paper is to formulate the canonical formalism on null hypersurfaces for the Maxwell electrodynamics. The set of the Poisson brackets relations for null variables of the Maxwell field is obtained. The asymptotic properties of the theory are investigated. The Poisson bracket relations for the news-functions of the Maxwell field are computed. The Hamiltonian form of the asymptotic Maxwell equations in terms of these news-functions is obtained.

A Null Space Control of Two Wheels Driven Mobile Manipulator Using Passivity Theory

Science.gov (United States)

Shibata, Tsuyoshi; Murakami, Toshiyuki

This paper describes a control strategy of null space motion of a two wheels driven mobile manipulator. Recently, robot is utilized in various industrial fields and it is preferable for the robot manipulator to have multiple degrees of freedom motion. Several studies of kinematics for null space motion have been proposed. However stability analysis of null space motion is not enough. Furthermore, these approaches apply to stable systems, but they do not apply unstable systems. Then, in this research, base of manipulator equips with two wheels driven mobile robot. This robot is called two wheels driven mobile manipulator, which becomes unstable system. In the proposed approach, a control design of null space uses passivity based stabilizing. A proposed controller is decided so that closed-loop system of robot dynamics satisfies passivity. This is passivity based control. Then, control strategy is that stabilizing of the robot system applies to work space observer based approach and null space control while keeping end-effector position. The validity of the proposed approach is verified by simulations and experiments of two wheels driven mobile manipulator.

Standard and Null Weak Values

OpenAIRE

Zilberberg, Oded; Romito, Alessandro; Gefen, Yuval

2013-01-01

Weak value (WV) is a quantum mechanical measurement protocol, proposed by Aharonov, Albert, and Vaidman. It consists of a weak measurement, which is weighed in, conditional on the outcome of a later, strong measurement. Here we define another two-step measurement protocol, null weak value (NVW), and point out its advantages as compared to WV. We present two alternative derivations of NWVs and compare them to the corresponding derivations of WVs.

Anti-optic-null medium: Achieving the optic-null medium effect by enclosing an air region with relatively low-anisotropy media

Science.gov (United States)

Sun, Fei; Liu, Yichao; He, Sailing

2016-07-01

A so-called anti-optic-null medium (anti-ONM), which can be utilized to cancel the optic-null medium (ONM) and create many novel optical illusions, is introduced and designed by transformation optics (TO). Optical separation illusions can be achieved with an anti-ONM. With the help of the anti-ONM, we can achieve the same optical illusions where ONM is required via a shelled structure filled with low anisotropic medium, which is easier to realize for some novel optical devices designed by TO and optical surface transformation. The special function of the anti-ONM will lead to a new way to design optical devices or simplify the material requirements. Overlapping illusions, and wave-front reshapers are designed to demonstrate the function of the proposed method.

Instabilities and the null energy condition

International Nuclear Information System (INIS)

Buniy, Roman V.; Hsu, Stephen D.H.

2006-01-01

We show that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. When applied to the dark energy, our results imply that w=p/ρ is unlikely to be less than -1. than -1

A conformal invariant model of localized spinning test particles

International Nuclear Information System (INIS)

Duval, C.; Centre National de la Recherche Scientifique, 13 - Marseille; Fliche, H.H.; Centre National de la Recherche Scientifique, 13 - Marseille

1977-02-01

A purely classical model of massless test particle with spin s is introduced as the dynamical system defined by the 10 dimensional 0(4,2) co-adjoint orbit with Casimir numbers (s 2 ,0,0). The Mathisson Papapetrou et al. equations of motion in a gravitational field are recovered, and moreover the particle appears to travel on null geodesics. Several implications are discussed

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

Directory of Open Access Journals (Sweden)

Petarpa Boonserm

2018-05-01

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

OBSERVATION OF MAGNETIC RECONNECTION AT A 3D NULL POINT ASSOCIATED WITH A SOLAR ERUPTION

International Nuclear Information System (INIS)

Sun, J. Q.; Yang, K.; Cheng, X.; Ding, M. D.; Zhang, J.

2016-01-01

Magnetic null has long been recognized as a special structure serving as a preferential site for magnetic reconnection (MR). However, the direct observational study of MR at null-points is largely lacking. Here, we show the observations of MR around a magnetic null associated with an eruption that resulted in an M1.7 flare and a coronal mass ejection. The Geostationary Operational Environmental Satellites X-ray profile of the flare exhibited two peaks at ∼02:23 UT and ∼02:40 UT on 2012 November 8, respectively. Based on the imaging observations, we find that the first and also primary X-ray peak was originated from MR in the current sheet (CS) underneath the erupting magnetic flux rope (MFR). On the other hand, the second and also weaker X-ray peak was caused by MR around a null point located above the pre-eruption MFR. The interaction of the null point and the erupting MFR can be described as a two-step process. During the first step, the erupting and fast expanding MFR passed through the null point, resulting in a significant displacement of the magnetic field surrounding the null. During the second step, the displaced magnetic field started to move back, resulting in a converging inflow and subsequently the MR around the null. The null-point reconnection is a different process from the current sheet reconnection in this flare; the latter is the cause of the main peak of the flare, while the former is the cause of the secondary peak of the flare and the conspicuous high-lying cusp structure.

Simple Fourier optics formalism for high-angular-resolution systems and nulling interferometry.

Science.gov (United States)

Hénault, François

2010-03-01

Reviewed are various designs of advanced, multiaperture optical systems dedicated to high-angular-resolution imaging or to the detection of exoplanets by nulling interferometry. A simple Fourier optics formalism applicable to both imaging arrays and nulling interferometers is presented, allowing their basic theoretical relationships to be derived as convolution or cross-correlation products suitable for fast and accurate computation. Several unusual designs, such as a "superresolving telescope" utilizing a mosaicking observation procedure or a free-flying, axially recombined interferometer are examined, and their performance in terms of imaging and nulling capacity are assessed. In all considered cases, it is found that the limiting parameter is the diameter of the individual telescopes. A final section devoted to nulling interferometry shows an apparent superiority of axial versus multiaxial recombining schemes. The entire study is valid only in the framework of first-order geometrical optics and scalar diffraction theory. Furthermore, it is assumed that all entrance subapertures are optically conjugated with their associated exit pupils.

Abnormal Activation of BMP Signaling Causes Myopathy in Fbn2 Null Mice.

Directory of Open Access Journals (Sweden)

Gerhard Sengle

2015-06-01

Full Text Available Fibrillins are large extracellular macromolecules that polymerize to form the backbone structure of connective tissue microfibrils. Mutations in the gene for fibrillin-1 cause the Marfan syndrome, while mutations in the gene for fibrillin-2 cause Congenital Contractural Arachnodactyly. Both are autosomal dominant disorders, and both disorders affect musculoskeletal tissues. Here we show that Fbn2 null mice (on a 129/Sv background are born with reduced muscle mass, abnormal muscle histology, and signs of activated BMP signaling in skeletal muscle. A delay in Myosin Heavy Chain 8, a perinatal myosin, was found in Fbn2 null forelimb muscle tissue, consistent with the notion that muscle defects underlie forelimb contractures in these mice. In addition, white fat accumulated in the forelimbs during the early postnatal period. Adult Fbn2 null mice are already known to demonstrate persistent muscle weakness. Here we measured elevated creatine kinase levels in adult Fbn2 null mice, indicating ongoing cycles of muscle injury. On a C57Bl/6 background, Fbn2 null mice showed severe defects in musculature, leading to neonatal death from respiratory failure. These new findings demonstrate that loss of fibrillin-2 results in phenotypes similar to those found in congenital muscular dystrophies and that FBN2 should be considered as a candidate gene for recessive congenital muscular dystrophy. Both in vivo and in vitro evidence associated muscle abnormalities and accumulation of white fat in Fbn2 null mice with abnormally activated BMP signaling. Genetic rescue of reduced muscle mass and accumulation of white fat in Fbn2 null mice was accomplished by deleting a single allele of Bmp7. In contrast to other reports that activated BMP signaling leads to muscle hypertrophy, our findings demonstrate the exquisite sensitivity of BMP signaling to the fibrillin-2 extracellular environment during early postnatal muscle development. New evidence presented here suggests that

Schwarzschild-de Sitter spacetime: The role of temperature in the emission of Hawking radiation

Science.gov (United States)

Pappas, Thomas; Kanti, Panagiota

2017-12-01

We consider a Schwarzschild-de Sitter (SdS) black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

Science.gov (United States)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

All the Four-Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory

International Nuclear Information System (INIS)

Cvetic, M.; Youm, D.

1995-01-01

We present the explicit form for all the four-dimensional, static, spherically symmetric solutions in (4+n)-d Abelian Kaluza-Klein theory by performing a subset of SO(2,n) transformations corresponding to four SO(1,1) boosts on the Schwarzschild solution, supplemented by SO(n)/SO(n-2) transformations. The solutions are parametrized by the mass M, Taub-NUT charge a, and n electric rvec Q and n magnetic rvec P charges. Nonextreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordstroem or Schwarzschild global space-time. Supersymmetric extreme black holes have a null or naked singularity, while nonsupersymmetric extreme ones have a global space-time of extreme Reissner-Nordstroem black holes. copyright 1995 The American Physical Society

Pattern Nulling of Linear Antenna Arrays Using Backtracking Search Optimization Algorithm

Directory of Open Access Journals (Sweden)

Kerim Guney

2015-01-01

Full Text Available An evolutionary method based on backtracking search optimization algorithm (BSA is proposed for linear antenna array pattern synthesis with prescribed nulls at interference directions. Pattern nulling is obtained by controlling only the amplitude, position, and phase of the antenna array elements. BSA is an innovative metaheuristic technique based on an iterative process. Various numerical examples of linear array patterns with the prescribed single, multiple, and wide nulls are given to illustrate the performance and flexibility of BSA. The results obtained by BSA are compared with the results of the following seventeen algorithms: particle swarm optimization (PSO, genetic algorithm (GA, modified touring ant colony algorithm (MTACO, quadratic programming method (QPM, bacterial foraging algorithm (BFA, bees algorithm (BA, clonal selection algorithm (CLONALG, plant growth simulation algorithm (PGSA, tabu search algorithm (TSA, memetic algorithm (MA, nondominated sorting GA-2 (NSGA-2, multiobjective differential evolution (MODE, decomposition with differential evolution (MOEA/D-DE, comprehensive learning PSO (CLPSO, harmony search algorithm (HSA, seeker optimization algorithm (SOA, and mean variance mapping optimization (MVMO. The simulation results show that the linear antenna array synthesis using BSA provides low side-lobe levels and deep null levels.

Partial null astigmatism-compensated interferometry for a concave freeform Zernike mirror

Science.gov (United States)

Dou, Yimeng; Yuan, Qun; Gao, Zhishan; Yin, Huimin; Chen, Lu; Yao, Yanxia; Cheng, Jinlong

2018-06-01

Partial null interferometry without using any null optics is proposed to measure a concave freeform Zernike mirror. Oblique incidence on the freeform mirror is used to compensate for astigmatism as the main component in its figure, and to constrain the divergence of the test beam as well. The phase demodulated from the partial nulled interferograms is divided into low-frequency phase and high-frequency phase by Zernike polynomial fitting. The low-frequency surface figure error of the freeform mirror represented by the coefficients of Zernike polynomials is reconstructed from the low-frequency phase, applying the reverse optimization reconstruction technology in the accurate model of the interferometric system. The high-frequency surface figure error of the freeform mirror is retrieved from the high-frequency phase adopting back propagating technology, according to the updated model in which the low-frequency surface figure error has been superimposed on the sag of the freeform mirror. Simulations verified that this method is capable of testing a wide variety of astigmatism-dominated freeform mirrors due to the high dynamic range. The experimental result using our proposed method for a concave freeform Zernike mirror is consistent with the null test result employing the computer-generated hologram.

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

Red hair is the null phenotype of MC1R.

Science.gov (United States)

Beaumont, Kimberley A; Shekar, Sri N; Cook, Anthony L; Duffy, David L; Sturm, Richard A

2008-08-01

The Melanocortin-1 Receptor (MC1R) is a G-protein coupled receptor, which is responsible for production of the darker eumelanin pigment and the tanning response. The MC1R gene has many polymorphisms, some of which have been linked to variation in pigmentation phenotypes within human populations. In particular, the p.D84E, p.R151C, p.R160W and p.D294 H alleles have been strongly associated with red hair, fair skin and increased skin cancer risk. These red hair colour (RHC) variants are relatively well described and are thought to result in altered receptor function, while still retaining varying levels of signaling ability in vitro. The mouse Mc1r null phenotype is yellow fur colour, the p.R151C, p.R160W and p.D294 H alleles were able to partially rescue this phenotype, leading to the question of what the true null phenotype of MC1R would be in humans. Due to the rarity of MC1R null alleles in human populations, they have only been found in the heterozygous state until now. We report here the first case of a homozygous MC1R null individual, phenotypic analysis indicates that red hair and fair skin is found in the absence of MC1R function.

Apoptosis in spermatogonia irradiated P53 null mice

International Nuclear Information System (INIS)

Streit-Bianchi, M.; Hendry, J.H.; Roberts, S.A.; Morris, J.D.; Durgaryan, A.A.

2007-01-01

Complete text of publication follows. The exposure of germ cells to ionizing radiations is of concern both from high-dose therapeutic exposures and from low doses causing deleterious trans-generational mutations. P53 protein plays an important role in cellular damage and is expressed in the testis normally during meiosis, its expression being localised to the preleptotene and early/mid pachytene spermatocytes. P53 null mice, heterozygotes possessing a 129 Sv/C57BL6 genetic background and B6D2F1 mice have been irradiated to 1 and 2 Gy single doses. Fractionated exposures of 1+1 Gy at 4 hours interval were also carried out. Apoptosis induction, spermatogonia and spermatocytes survival were assessed by microscope analysis of histological samples at 4 to 96 hours after irradiation in time-course experiments. The same end-points were also assessed at 72 and 96 hours after irradiation to single doses in the region between 20cGy to 2Gy. A dose dependent level of p53 expression was observed at 4 hours after irradiation to 1 and 2 Gy which returned to normal level by 24 hours. Our data support a two process mode of apoptosis with a first wave around 12 hours followed by a second wave at 2-3 days. The first wave apoptosis is substantially reduced in p53 null mice whereas the second wave is reduced in B6D2F1 mice. The initial increase in apoptosis was delayed in some stages of the of germ cells development which were identified by the spermatids shape. Clear correlation exists between apoptosis and survival assessed in stage XI-XII Tubules 72 hours after irradiation. The data are in agreement with other data in literature indicating that irradiated spermatogonia die through apoptosis. The lack of apoptosis observed in p53 null mice results in a very high survival rate of daughter cells assessed later. Theses spermatocytes and the following progenitor cells are likely to carry mutations as most will not die in the smaller second wave of apoptosis observed 3 days after