Stability under radiation reaction of circular equatorial orbits around Kerr black holes

We examine the evolution, under gravitational radiation reaction, of slightly eccentric equatorial orbits of point particles around Kerr black holes. Our method involves numerical integration of the Sasaki-Nakamura equation. It is discovered that such orbits decrease in eccentricity throughout most of the inspiral, until shortly before the innermost stable circular orbit (ISCO), when a critical radius $r_{\text{crit}}$ is reached beyond which the inspiralling orbits increase in eccentricity. It is shown that the number of orbits remaining in this last (eccentricity increasing) phase of the inspiral is an order of magnitude less for prograde orbits around rapidly spinning black holes than for retrograde orbits. In the extreme limit of a Kerr black hole with spin parameter $a=1$, this critical radius descends into the ``throat'' of the black hole.