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Chandrachur Chakraborty  One of the best experts on this subject based on the ideXlab platform.

inner most stable circular orbits in extremal and non extremal kerr taub nut Spacetimes
European Physical Journal C, 2014CoAuthors: Chandrachur ChakrabortyAbstract:We study causal geodesics in the equatorial plane of the extremal Kerr–TaubNUT Spacetime, focusing on the innermost stable circular orbit (ISCO), and we compare its behavior with extant results for the ISCO in the extremal Kerr Spacetime. Calculations of the radii of the direct ISCO, its Kepler frequency, and the rotational velocity show that the ISCO coincides with the horizon in the exactly extremal situation. We also study geodesics in the strong nonextremal limit, i.e., in the limit of a vanishing Kerr parameter (i.e., for TaubNUT and massless TaubNUT Spacetimes as special cases of this Spacetime). It is shown that the radius of the direct ISCO increases with NUT charge in TaubNUT Spacetime. As a corollary, it is shown that there is no stable circular orbit in massless NUT Spacetimes for timelike geodesics.

inner most stable circular orbits in extremal and non extremal kerr taub nut Spacetimes
arXiv: General Relativity and Quantum Cosmology, 2013CoAuthors: Chandrachur ChakrabortyAbstract:We study causal geodesics in the equatorial plane of the extremal KerrTaubNUT Spacetime, focusing on the Innermost Stable Circular Orbit (ISCO),and compare its behaviour with extant results for the ISCO in the extremal Kerr Spacetime. Calculation of the radii of the direct ISCO, its Kepler frequency, and rotational velocity show that the ISCO coincides with the horizon in the exactly extremal situation. We also study geodesics in the strong {\it non}extremal limit, i.e., in the limit of vanishing Kerr parameter (i.e., for TaubNUT and massless TaubNUT Spacetimes as special cases of this Spacetime). It is shown that the radius of the direct ISCO increases with NUT charge in TaubNUT Spacetime. As a corollary, it is shown that there is no stable circular orbit in massless NUT Spacetimes for timelike geodesics.
Ingemar Eriksson  One of the best experts on this subject based on the ideXlab platform.

the chevreton tensor and einstein maxwell Spacetimes conformal to einstein spaces
Classical and Quantum Gravity, 2007CoAuthors: Goran Bergqvist, Ingemar ErikssonAbstract:In this paper, we characterize the sourcefree Einstein–Maxwell Spacetimes which have a tracefree Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the Spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein–Maxwell Spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these Spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the Spacetime must be conformally Ricciflat and all such solutions are known. In the nonnull case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein–Maxwell Spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the Spacetime is conformal to a Cspace. The nonaligned Einstein–Maxwell Spacetimes with vanishing Bach tensor are conformally Cspaces, but none of them are conformal to Einstein spaces.

the chevreton tensor and einstein maxwell Spacetimes conformal to einstein spaces
arXiv: General Relativity and Quantum Cosmology, 2007CoAuthors: Goran Bergqvist, Ingemar ErikssonAbstract:In this paper we characterize the sourcefree EinsteinMaxwell Spacetimes which have a tracefree Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pureradiation type and that it restricts the Spacetimes to Petrov types \textbf{N} or \textbf{O}. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all EinsteinMaxwell Spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these Spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the Spacetime must be conformally Ricciflat and all such solutions are known. In the nonnull case, since the general solution is not known on closed form, we settle with giving the integrability conditions in the general case, but we do give new explicit examples of EinsteinMaxwell Spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the Spacetime is conformal to a $C$space. The nonaligned EinsteinMaxwell Spacetimes with vanishing Bach tensor are conformally $C$spaces, but none of them are conformal to Einstein spaces.
Christian Pfeifer  One of the best experts on this subject based on the ideXlab platform.

berwald Spacetimes and very special relativity
Physical Review D, 2018CoAuthors: Andrea Fuster, Cornelia Pabst, Christian PfeiferAbstract:In this work, we study Berwald Spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of Spacetimes that are nonflat generalizations of the very special relativity (VSR) line element, which we call ``very general relativity'' (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) Spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR Spacetime.

radar orthogonality and radar length in finsler and metric Spacetime geometry
Physical Review D, 2014CoAuthors: Christian PfeiferAbstract:The radar experiment connects the geometry of Spacetime with an observers measurement of spatial length. We investigate the radar experiment on Finsler Spacetimes which leads to a general definition of radar orthogonality and radar length. The directions radar orthogonal to an observer form the spatial equal time surface an observer experiences and the radar length is the physical length the observer associates to spatial objects. We demonstrate these concepts on a forth order polynomial Finsler Spacetime geometry which may emerge from area metric or premetric linear electrodynamics or in quantum gravity phenomenology. In an explicit generalization of Minkowski Spacetime geometry we derive the deviation from the Euclidean spatial length measure in an observers rest frame explicitly.

the finsler Spacetime framework backgrounds for physics beyond metric geometry
2013CoAuthors: Christian PfeiferAbstract:The fundamental structure on which physics is described is the geometric Spacetime back ground provided by a four dimensional manifold equipped with a Lorentzian metric. Most im portantly the Spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of Spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler Spacetime framework and ensure that the threefold role of the geometry of Spacetime in physics is not changed. The geometry of Finsler Spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler Spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our non metric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our welldefined Finsler Spacetime geometry we are able to derive dynamics for the nonmetric Finslerian geometry of Spacetime from an action principle, obtained from the Einstein–Hilbert action, for the first time. We can complete the dynamics to a nonmetric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler Spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the nonmetric Spacetime geometry. Physi cal consequence derived on the basis of our Finsler Spacetime are: a possible solution to the flyby anomaly in the solar system; the possible dependence of the speed of light on the relative motion between the observer and the light ray; modified dispersion relation and possible propa gation of particle modes faster than light and the propagation of light on Finsler nullgeodesics. Our Finsler Spacetime framework is the first extension of the framework of general rela tivity based on nonmetric Finslerian geometry which provides causality, observers and their measurements and gravity from a Finsler geometric Spacetime structure and yields a viable background on which action based physical field theories can be defined
Junji Jia  One of the best experts on this subject based on the ideXlab platform.

the perturbative approach for the weak deflection angle
European Physical Journal C, 2020CoAuthors: Junji JiaAbstract:Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity v in arbitrary static and spherically symmetric Spacetimes and in equatorial plane of arbitrary static and axisymmetric Spacetimes. We show that the expansion in the large closest approach $$x_0$$ limit depends on the asymptotic behavior of the metric functions only, and the generated integrand is always integrable, resulting in a deflection angle in a series form of either $$x_0$$ or b, the impact parameter. Using this method, the deflection angles as series of both $$x_0$$ and b are found in Schwarzschild, Reissner–Nordstrom and Kerr–Newman Spacetimes to 17th, 15th and 6th orders respectively, for both lightrays and particles with general velocity. The effects of the impact parameter, velocity and other parameters of the spacatimes are briefly analyzed. Moreover, we show that for Spacetimes whose metric functions are only asymptotically known, the deflection angle in the weak field limit can also be calculated. Furthermore, it is shown that the deflection angle in general static and spherically symmetric Spacetime and equatorial plane of static and axisymmetric Spacetime to the lowest nontrivial order, depends only on the impact parameter, velocity of the particle, and the effective ADM mass of the Spacetime but not on other parameters such as charge or angular momentum. These deflection angles are used in an exact gravitational lensing equation and the corresponding apparent angles of the images of the source are also solved perturbatively.

existence and stability of circular orbits in general static and spherically symmetric Spacetimes
General Relativity and Gravitation, 2018CoAuthors: Junji Jia, Jiawei Liu, Xionghui Liu, Xiankai Pang, Yaoguang Wang, Nan YangAbstract:The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) Spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a necessary and sufficient condition on the metric function for the existence of timelike COs in SSS Spacetimes. After analyzing the asymptotic behavior of the metric, we then show that asymptotic flat SSS Spacetime that corresponds to a negative Newtonian potential at large r will always allow the existence of CO. The stability of the CO in a general SSS Spacetime is then studied using the Lyapunov exponent method. Two sufficient conditions on the (in)stability of the COs are obtained. For null geodesics, a sufficient condition on the metric function for the (in)stability of null CO is also obtained. We then illustrate one powerful application of these results by showing that three SSS Spacetimes whose metric function is not completely known will allow the existence of timelike and/or null COs. We also used our results to assert the existence and (in)stabilities of a number of known SSS metrics.
Ghulam Shabbir  One of the best experts on this subject based on the ideXlab platform.

CLASSIFICATION OF CYLINDRICALLY SYMMETRIC STATIC SpacetimeS ACCORDING TO THEIR KILLING VECTOR FIELDS IN TELEPARALLEL THEORY OF GRAVITATION
Modern Physics Letters A, 2010CoAuthors: Ghulam Shabbir, Suhail KhanAbstract:In this paper we classify cylindrically symmetric static Spacetimes according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 3, 4, 6 or 10 which are the same in numbers as in general relativity. In case of 3, 4 or 6 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of r. In the case of 10 Killing vector fields the Spacetime becomes Minkowski Spacetime and all the torsion components are zero. The Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. It is important to note that this classification also covers the plane symmetric static Spacetimes.

proper projective symmetry in plane symmetric static Spacetimes
Classical and Quantum Gravity, 2004CoAuthors: Ghulam ShabbirAbstract:An approach is developed to study proper projective vector fields in plane symmetric static Spacetimes. It is shown that the special class of the above Spacetime admits proper projective vector fields.