Quasi-local studies of the particle surfaces and their stability in general spacetimes

TL;DR

This paper introduces a new quasi-local framework for analyzing particle surfaces and their stability in general spacetimes, extending previous definitions to include spherical orbits in stationary spacetimes and deriving evolution equations for ISCO.

Contribution

It provides novel quasi-local definitions of particle surfaces and their stability, enabling analysis of circular orbits and ISCO evolution in general spacetimes, including cases not covered by prior definitions.

Findings

Consistent results with previous studies on circular orbits

New criteria for particle surfaces in spacetimes without gravity

Derived evolution equations for ISCO in general spacetimes

Abstract

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.