Effect of gravitational radiation reaction on circular orbits around a spinning black hole

TL;DR

This paper calculates how gravitational radiation reaction affects circular orbits around a spinning black hole, showing the orbit shrinks and the orbital plane slowly aligns with the black hole's spin.

Contribution

It provides a leading-order analytical computation of radiation reaction effects on circular Kerr orbits, including orbital shrinkage and slow plane realignment.

Findings

Orbit shrinks due to radiation reaction

Orbital plane gradually aligns with black hole spin

Orbit remains circular during evolution

Abstract

The effect of gravitational radiation reaction on circular orbits around a spinning (Kerr) black hole is computed to leading order in $S$ (the magnitude of the spin angular momentum of the hole) and in the strength of gravity $M/r$ (where $M$ is the mass of the black hole, $r$ is the orbital radius, and $G=c=1$). The radiation reaction makes the orbit shrink but leaves it circular, and drives the orbital plane very slowly toward antialignment with the spin of the hole: $\tan (\iota /2) = \tan (\iota_0 /2) [1+(61/72)(S/M^2) (M/r)^{3/2}]$, where $\iota$ is the angle between the normal to the orbital plane and the spin direction, and $\iota_0$ is the initial value of $\iota$, when $r$ is very large.