  A major focus of much current research in gravitation theory is on
understanding how radiation reaction drives the evolution of a binary system,
particularly in the extreme mass ratio limit. Such research is of direct
relevance to gravitational-wave sources for space-based detectors (such as
LISA). We present here a study of the radiative evolution of circular (i.e.,
constant Boyer-Lindquist coordinate radius), non-equatorial Kerr black hole
orbits. Recent theorems have shown that, at least in an adiabatic evolution,
such orbits evolve from one circular configuration into another, changing only
their radius and inclination angle. This constrains the system's evolution in
such a way that the change in its Carter constant can be deduced from knowledge
of gravitational wave fluxes propagating to infinity and down the black hole's
horizon. Thus, in this particular case, a local radiation reaction force is not
needed. In accordance with post-Newtonian weak-field predictions, we find that
inclined orbits radiatively evolve to larger inclination angles (although the
post-Newtonian prediction overestimates the rate of this evolution in the
strong field by a factor $\lesssim 3$). We also find that the gravitational
waveforms emitted by these orbits are rather complicated, particularly when the
hole is rapidly spinning, as the radiation is influenced by many harmonics of
the orbital frequencies.
