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

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 $M\mathrm{/}r$ (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: $\tan (\iota \mathrm{/}2)=\tan ({\iota }_0\mathrm{/}2)[1+(61\mathrm{/}72)(S\mathrm{/}{M}^2)(M\mathrm{/}r{)}^{3\mathrm{/}2}]$, 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.