Effect of gravitational radiation reaction on nonequatorial orbits around a Kerr black hole

TL;DR

This paper analyzes how gravitational radiation reaction influences the evolution of inclined and eccentric orbits around a Kerr black hole, revealing that circular orbits stay circular and providing leading-order evolution equations for other orbits.

Contribution

It introduces a leading-order calculation of the orbital parameter evolution under gravitational radiation reaction for inclined and eccentric orbits around a Kerr black hole.

Findings

Circular orbits remain circular under radiation reaction.

Inclined orbits tend to increase in inclination as the semi-major axis decreases.

Eccentricity decreases as the orbit shrinks.

Abstract

The effect of gravitational radiation reaction on orbits around a spinning black hole is analyzed. Such orbits possess three constants of motion: $\iota$, $e$, and $a$, which correspond, in the Newtonian limit of the orbit being an ellipse, to the inclination angle of the orbital plane to the hole's equatorial plane, the eccentricity, and the semi-major axis length, respectively. First, it is argued that circular orbits ($e=0$) remain circular under gravitational radiation reaction. Second, for elliptical orbits (removing the restriction of $e=0$), the evolution of $\iota$, $e$, and $a$ is computed to leading order in $S$ (the magnitude of the spin angular momentum of the hole) and in $M/a$, where $M$ is the mass of the black hole. As $a$ decreases, $\iota$ increases and $e$ decreases.