Deflection angle of a light ray reflected by a general marginally unstable photon sphere in a strong deflection limit

Tsukamoto, Naoki

doi:10.48550/arxiv.2008.12244

Cited by 2 publications

(2 citation statements)

References 72 publications

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“…Furthermore, it has recently been shown [25,26] that the existence of KT can be related to important characteristics of spacetime, such as photon spheres and their generalizations: fundamental photon surfaces [27][28][29][30][31][32][33][34][35][36][37][38], which are compact submanifolds paved by null geodesics. Such surfaces are important for strong gravitational lensing and black hole shadows [39][40][41][42][43][44][45][46][47][48][49][50][51]. They are equally useful in the analysis of the black hole uniqueness [52][53][54][55][56][57][58][59][60][61] and in deriving the area bounds [62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Slice-reducible conformal Killing tensors, photon surfaces and shadows

Kobialko,

Bogush,

Gal'tsov

2022

Preprint

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We generalize our recent method for constructing Killing tensors of the second rank to conformal Killing tensors. The method is intended for foliated spacetimes of arbitrary dimension m, which have a set of conformal Killing vectors. It applies to foliations of a more general structure than in previous literature. The basic idea is to start with reducible Killing tensors in slices constructed from a set of conformal Killing vectors and the induced metric, and then lift them to the whole manifold. Integrability conditions are derived that ensure this, and a constructive lifting procedure is presented. The resulting conformal Killing tensor may be irreducible. It is shown that subdomains of foliation slices suitable for the method are fundamental photon surfaces if some additional photon region inequality is satisfied. Thus our procedure also opens the way to obtain a simple general analytical expression for the boundary of the gravitational shadow. We apply this technique to electrovacuum, and N = 2, 4, 8 supergravity black holes, providing a new easy way to establish the existence of exact and conformal Killing tensors.

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Section: Introductionmentioning

confidence: 99%

Slice-reducible conformal Killing tensors, photon surfaces and shadows

Kobialko,

Bogush,

Gal'tsov

2022

Preprint

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“…This purely geometric property can serve as a constructive definition for analyzing photon surfaces instead of solving geodesic equations and plays a decisive role in the analysis of the black hole uniqueness [24][25][26][27][28][29][30][31][32][33] and area bounds [34][35][36]. Photon surfaces find applications in the description of optical properties and gravitational shadows [37][38][39][40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

The geometry of massive particle surfaces

Kobialko¹,

Bogush²,

Gal’tsov³

2022

Preprint

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We propose a generalization of Claudel, Virbhadra, and Ellis photon surfaces to the case of massive charged particles, considering a timelike hypersurface such that any worldline of a particle with mass m, electric charge q and fixed total energy E, initially touching it, will remain in this hypersurface forever. This definition does not directly appeal to the equations of motion, but instead make use of partially umbilic nature of the surface geometry. Such an approach should be especially useful in the case of non-integrable equations of motion. It may be applied in the theory of non-thin accretion discs, and also may serve a new tool for some general problems, such as uniqueness theorems, Penrose inequalities and hidden symmetries. The condition for the stability of the worldlines is derived, which reduces to differentiation along the flow of surfaces of a certain energy. We consider a number of examples of electrovacuum and dilaton solutions, find conditions for marginally stable orbits, regions of stable or unstable spherical orbits, stable and unstable photon surfaces, and solutions satisfying the no-force condition.

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Deflection angle of a light ray reflected by a general marginally unstable photon sphere in a strong deflection limit

Cited by 2 publications

References 72 publications

Slice-reducible conformal Killing tensors, photon surfaces and shadows

Slice-reducible conformal Killing tensors, photon surfaces and shadows

The geometry of massive particle surfaces

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