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General Relativity and Quantum Cosmology

arXiv:2204.05593 (gr-qc)
[Submitted on 12 Apr 2022 (v1), last revised 19 Aug 2022 (this version, v3)]

Title:Light propagation in a plasma on an axially symmetric and stationary spacetime: Separability of the Hamilton-Jacobi equation and shadow

Authors:Barbora Bezdekova, Volker Perlick, Jiri Bicak
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Abstract:The properties of light rays around compact objects surrounded by a plasma are affected by both strong gravitational fields described by a general-relativistic spacetime and by a dispersive and refractive medium, characterized by the density distribution of the plasma. We study these effects employing the relativistic Hamiltonian formalism under the assumption of stationarity and axisymmetry. The necessary and sufficient conditions on the metric and on the plasma frequency are formulated, such that the rays can be analytically determined from a fully separated Hamilton-Jacobi equation. We demonstrate how these results allow to analytically calculate the photon region and the shadow, if they exist. Several specific examples are discussed in detail: the "hairy" Kerr black holes, the Hartle-Thorne spacetime metrics, the Melvin universe, and the Teo rotating traversable wormhole. In all of these cases a plasma medium is present as well.
Comments: to appear in Journal of Mathematical Physics
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:2204.05593 [gr-qc]
  (or arXiv:2204.05593v3 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.2204.05593
Related DOI: https://doi.org/10.1063/5.0106433

Submission history

From: Barbora Bezděková [view email]
[v1] Tue, 12 Apr 2022 07:48:59 UTC (84 KB)
[v2] Sun, 10 Jul 2022 14:34:47 UTC (514 KB)
[v3] Fri, 19 Aug 2022 09:52:46 UTC (86 KB)
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