Nearly horizon skimming orbits of Kerr black holes

An unusual set of orbits about extreme Kerr black holes resides at the Boyer-Lindquist radius $r = M$, the coordinate of the hole's event horizon. These ``horizon skimming'' orbits have the property that their angular momentum $L_z$ {\it increases} with inclination angle, opposite to the familiar behavior one encounters at larger radius. In this paper, I show that this behavior is characteristic of a larger family of orbits, the ``nearly horizon skimming'' (NHS) orbits. NHS orbits exist in the very strong field of any black hole with spin $a\agt 0.952412M$. Their unusual behavior is due to the locking of particle motion near the event horizon to the hole's spin, and is therefore a signature of the Kerr metric's extreme strong field. An observational hallmark of NHS orbits is that a small body spiraling into a Kerr black hole due to gravitational-wave emission will be driven into orbits of progressively smaller inclination angle, toward the equator. This is in contrast to the ``normal'' behavior. For circular orbits, the change in inclination is very small, and unlikely to be of observational importance. I argue that the change in inclination may be considerably larger when one considers the evolution of inclined eccentric orbits. If this proves correct, then the gravitational waves produced by evolution through the NHS regime may constitute a very interesting and important probe of the strong-field nature of rotating black holes.