Stability under radiation reaction of circular equatorial orbits around Kerr black holes

TL;DR

This paper investigates how gravitational radiation reaction affects the eccentricity of equatorial orbits around Kerr black holes, revealing a critical radius where eccentricity behavior reverses, especially in rapidly spinning black holes.

Contribution

It introduces a numerical method to analyze orbit evolution under radiation reaction and identifies a critical radius affecting eccentricity trends in Kerr black hole orbits.

Findings

Eccentricity generally decreases during inspiral until near the ISCO.

A critical radius exists where eccentricity begins to increase.

Rapidly spinning black holes have a smaller last eccentric orbit phase.

Abstract

We examine the evolution, under gravitational radiation reaction, of slightly eccentric equatorial orbits of point particles around Kerr black holes. Our method involves numerical integration of the Sasaki-Nakamura equation. It is discovered that such orbits decrease in eccentricity throughout most of the inspiral, until shortly before the innermost stable circular orbit (ISCO), when a critical radius $r_{\text{crit}}$ is reached beyond which the inspiralling orbits increase in eccentricity. It is shown that the number of orbits remaining in this last (eccentricity increasing) phase of the inspiral is an order of magnitude less for prograde orbits around rapidly spinning black holes than for retrograde orbits. In the extreme limit of a Kerr black hole with spin parameter $a=1$, this critical radius descends into the ``throat'' of the black hole.