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

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(\ensuremath{\iota}/2)=tan(${\mathrm{\ensuremath{\iota}}}_{0}$/2)[1+(61/72)(S/${\mathit{M}}^{2}$)(M/r${)}^{3/2}$], where \ensuremath{\iota} is the angle between the normal to the orbital plane and the spin direction, and ${\mathrm{\ensuremath{\iota}}}_{0}$ is the initial value of \ensuremath{\iota}, when r is very large.