https://doi.org/10.1140/epjc/s10052-024-12954-9
Regular Article – Theoretical Physics
A generalization of photon sphere based on escape/capture cone
1
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan
2
Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos, Universitat de Barcelona, 08028, Barcelona, Spain
3
Department of Mathematics, Nagoya University, 464-8602, Nagoya, Japan
4
Kobayashi-Maskawa Institute, Nagoya University, 464-8602, Nagoya, Japan
5
Department of Physics, Osaka Metropolitan University, 558-8585, Osaka, Japan
6
Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 558-8585, Osaka, Japan
7
Division of Science, School of Science and Engineering, Tokyo Denki University, 350-0394, Saitama, Japan
a
masaya.amo@yukawa.kyoto-u.ac.jp
Received:
5
May
2024
Accepted:
27
May
2024
Published online:
25
June
2024
In general asymptotically flat spacetimes, bearing the null geodesics reaching the future null infinity in mind, we propose new concepts, the “dark horizons” (outer dark horizon and inner dark horizon) as generalizations of the photon sphere. They are defined in terms of the structure of escape/capture cones of photons with respect to a unit timelike vector field to capture the motion of light sources. More specifically, considering a two-sphere that represents a set of emission directions of photons, the dark horizons are located at positions where a hemisphere is marginally included in the capture and escape cones, respectively. In addition, our definition succeeds in incorporating relativistic beaming effect. We show that the dark horizon is absent in the Minkowski spacetime, while they exist in spacetimes with black hole(s) under a certain condition. We derive the general properties of the dark horizons in spherically symmetric spacetimes and explicitly calculate the locations of the dark horizons in the Vaidya spacetime and the Kerr spacetime. In particular, in the Kerr spacetime, the outer dark horizon coincides with the shadow observed from infinity on the rotation axis.
© The Author(s) 2024
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