Photon regions in stationary axisymmetric spacetimes and umbilic conditions

Kobialko, Kirill; Gal’tsov, D.V.

doi:10.48550/arxiv.2110.04610

Cited by 3 publications

(9 citation statements)

References 29 publications

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“…Somewhat surprisingly, the equations that determine the null geodesics and the integrability conditions for the second-rank KT equations turn out to be related [23,24]. 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].…”

Section: Introductionmentioning

confidence: 95%

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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: 95%

“…Recall the main ideas underlying the concept of FPS [37,38]. Consider the case of a manifold with two conformal Killing vectors spanning a timelike surface (ǫ = +1, det(G ab ) < 0).…”

Section: A Photon Submanifoldsmentioning

confidence: 99%

Slice-reducible conformal Killing tensors, photon surfaces and shadows

Kobialko,

Bogush,

Gal'tsov

2022

Preprint

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“…After one has determined the acceptable range of the impact parameter ρ, we can proceed to the determination of the fundamental photon surfaces (FPS) [47,[88][89][90] which play a key role in the process of shadow formation since they capture null geodesics with a fixed value of the impact parameter. Consider an arbitrary hypersurface S of the form r = f (θ).…”

Section: B Photon Regionmentioning

confidence: 99%

“…Consider an arbitrary hypersurface S of the form r = f (θ). To determine the fundamental photon surfaces and regions, we will use the master equation [89,90] with the vector ξ µ normal to S, i.e.,…”

Section: B Photon Regionmentioning

confidence: 99%

Photon surfaces, shadows and accretion disks in gravity with minimally coupled scalar field

Bogush,

Gal'tsov,

Gyulchev

et al. 2022

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In this article, we conduct a sequential study of possible observable images of black hole simulators described by two recently obtained rotating geometries in Einstein gravity, minimally coupled to a scalar field. One of them, "Kerr-like" (KL), can be seen as a legitimate alternative to the rotating Fisher-Janis-Newman-Winicour (FJNW) solution, and the other (TSL) is a scalar generalization of the Tomimatsu-Sato solution. Unlike the previous version of the rotating FJNW, these solutions do indeed satisfy the system's equations of motion. Our study includes both analytical and numerical calculations of equatorial circular orbits, photon regions, gravitational shadows, and radiation from thin accretion disks for various values of the object's angular momentum and scalar charge. The TSL solution was found to simulate Kerr for all valid parameter values with high accuracy. The maximum difference between the deviations of shadows from a circle for the Kerr and TSL cases does not exceed 1% and fits into the experimental observational data M87 * . However, near-extreme objects show two times smaller peak values of the observed outflow luminosity of the accretion disk than for the Kerr black hole. The KL solution cannot be ruled out by the experimental data for small values of the scalar charge either. As the scalar charge increases, the optical properties change dramatically. The shadow can become multiply connected, strongly oblate, and the photon region does not hide the singularity, so it should be classified as a strong singularity.

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“…The shadows of black holes and images of accretion disks around them are now released in the radio and optical ranges and they are associated with the properties of null geodesics in strong gravitational fields [3][4][5][6][7][8][9][10]. The most important role in the mathematical understanding of shadows is played by the concept of characteristic photon surfaces [11][12][13][14][15][16][17][18][19][20][21] -timelike hypersurfaces, where bounded photon trajectories are lined up.…”

Section: Introductionmentioning

confidence: 99%

The geometry of massive particle surfaces

Kobialko¹,

Bogush²,

Gal’tsov³

2022

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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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Photon regions in stationary axisymmetric spacetimes and umbilic conditions

Abstract: We present the fundamentals of the recently proposed geometric description [1] of photon regions in terms of foliation into fundamental photon hypersurfaces, which satisfies the umbilic condition for the subbundle of the tangent bundle defined by the generalized impact parameter.

Cited by 3 publications

References 29 publications

Slice-reducible conformal Killing tensors, photon surfaces and shadows

Slice-reducible conformal Killing tensors, photon surfaces and shadows

Photon surfaces, shadows and accretion disks in gravity with minimally coupled scalar field

The geometry of massive particle surfaces

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