The evolutions of the innermost stable circular orbits in dynamical spacetimes

TL;DR

This paper develops a method to analyze the evolution of innermost stable circular orbits (ISCOs) in dynamical spacetimes, generalizing previous techniques and applying them to various spacetime models to understand their behavior.

Contribution

It introduces a generalized method for studying ISCO evolution in dynamical spacetimes based on conserved orbital angular momentum, extending previous static spacetime approaches.

Findings

Method successfully applied to Vaidya spacetime

Method consistent with photon sphere evolutions

Provides reasonable and comparable results in dynamical spacetimes

Abstract

In this paper, we studied the evolutions of the innermost stable circular orbits (ISCOs) in dynamical spacetimes. At first, we reviewed the method to obtain the ISCO in Schwarzschild spacetime by varying its conserved orbital angular momentum. Then, we demonstrated this method is equivalent to the effective potential method in general static and stationary spacetimes. Unlike the effective potential method, which depends on the presence of the conserved orbital energy, this method requires the existence of conserved orbital angular momentum in spacetime. So it can be easily generalized to the dynamical spacetimes where there exists conserved orbital angular momentum. From this generalization, we studied the evolutions of the ISCOs in Vaidya spacetime, Vaidya-AdS spacetime and the slow rotation limit of Kerr-Vaidya spacetime. The results given by these examples are all reasonable and can be compared with the evolutions of the photon spheres in dynamical spacetime