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

Fintan D. Ryan
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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: $\tan (ι/2) = \tan (ι_0 /2) [1+(61/72)(S/M^2) (M/r)^{3/2}]$, where $ι$ is the angle between the normal to the orbital plane and the spin direction, and $ι_0$ is the initial value of $ι$, when $r$ is very large.

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Fintan D. Ryan. 1995-06-08. Effect of gravitational radiation reaction on circular orbits around a spinning black hole. https://doi.org/10.1103/physrevd.52.r3159

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