  Inspiral of compact stellar remnants into massive black holes (MBHs) is
accompanied by the emission of gravitational waves at frequencies that are
potentially detectable by space-based interferometers. Event rates computed
from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due
to uncertaintities about the rate coefficients. Here we present results from
direct integration of the post-Newtonian N-body equations of motion descrbing
dense clusters of compact stars around Schwarzschild MBHs. These simulations
embody an essentially exact (at the post-Newtonian level) treatment of the
interplay between stellar dynamical relaxation, relativistic precession, and
gravitational-wave energy loss. The rate of capture of stars by the MBH is
found to be greatly reduced by relativistic precession, which limits the
ability of torques from the stellar potential to change orbital angular
momenta. Penetration of this "Schwarzschild barrier" does occasionally occur,
resulting in capture of stars onto orbits that gradually inspiral due to
gravitational wave emission; we discuss two mechanisms for barrier penetration
and find evidence for both in the simulations. We derive an approximate formula
for the capture rate, which predicts that captures would be strongly disfavored
from orbits with semi-major axes below a certain value; this prediction, as
well as the predicted rate, are verified in the N-body integrations. We discuss
the implications of our results for the detection of extreme-mass-ratio
inspirals from galactic nuclei with a range of physical properties.
