https://doi.org/10.1140/epjc/s10052-022-11143-w
Regular Article - Theoretical Physics
Quasi-local studies of the particle surfaces and their stability in general spacetimes
College of Mathematics and Physics, Chengdu University of Technology, 610059, Chengdu, Sichuan, China
Received:
27
June
2022
Accepted:
16
December
2022
Published online:
20
January
2023
In this paper, enlightened by the definition of the photon surface given by Claudel, Virbhadra and Ellis, we give a quasi-local definition of the particle surface. From this definition, one can study the evolution of the circular orbits in general spacetime. Especially, we pointed out that this definition can be used to get the spherical circular orbits in stationary spacetimes which cannot be got by the definition of Claudel, Virbhadra and Ellis. Further, we give a condition to exclude the particle surface in spacetime without gravity. Simultaneously, we give a quasi-local definition of the stability of the particle surface in general spacetime. From this definition, one can get the evolution equation of the innermost stable circular orbit (ISCO) in general spacetime. To verify the correctness of these definitions, we studied the circular orbits in some special cases and the results are all consistent with the previous results.
© The Author(s) 2023
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