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/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 (/2) =tan (₀/2) 1+ (61/72) (S/M^2) (M/r) ^3/2, where is the angle between the normal to the orbital plane and the spin direction, and ₀ is the initial value of, when r is very large.