Effect of gravitational radiation reaction on nonequatorial orbits around a Kerr black hole.

Abstract

The effect of gravitational radiation reaction on orbits around a spinning black hole is analyzed. Such orbits possess three constants of motion: $\ensuremath{\iota}$, $e$, and $a$, which correspond, in the Newtonian limit of the orbit being an ellipse, to the inclination angle of the orbital plane to the hole's equatorial plane, the eccentricity, and the semimajor axis length, respectively. First, it is argued that circular orbits ($e=0$) remain circular under gravitational radiation reaction. Second, for elliptical orbits (removing the restriction of $e=0$), the evolution of $\ensuremath{\iota}$, $e$, and $a$ is computed to leading order in $S$ (the magnitude of the spin angular momentum of the hole) and in $\frac{M}{a}$, where $M$ is the mass of the black hole. As $a$ decreases, $\ensuremath{\iota}$ increases and $e$ decreases.