Nonradial stability of marginal stable circular orbits in stationary axisymmetric spacetimes

TL;DR

This paper investigates the stability of marginal stable circular orbits in stationary axisymmetric spacetimes, analyzing how perturbations affect orbit stability, with applications to Kerr, Majumdar-Papapetrou, and modified black hole metrics.

Contribution

It introduces a method to analyze nonradial perturbations of MSCOs and applies it to various solutions, revealing stability properties and implications for modified black hole models.

Findings

Vertical perturbations can destabilize orbits previously stable against radial perturbations.

In the Johannsen-Psaltis model, the last stable orbit may be larger than the traditional ISCO.

The approach clarifies stability criteria for orbits in complex spacetime geometries.

Abstract

We study linear nonradial perturbations and stability of a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a test particle in stationary axisymmetric spacetimes which possess a reflection symmetry with respect to the equatorial plane. The proposed approach is applied to Kerr solution and Majumdar-Papapetrou solution to Einstein equation. Finally, we reexamine MSCOs for a modified metric of a rapidly spinning black hole that has been recently proposed by Johannsen and Psaltis [PRD, 83, 124015 (2011)]. We show that, for the Johannsen and Psaltis's model, circular orbits that are stable against radial perturbations for some parameter region become unstable against vertical perturbations. This suggests that the last circular orbit for this model may be larger than the ISCO.