  The long-term evolution of massive black hole binaries at the centers of
galaxies is studied in a variety of physical regimes, with the aim of resolving
the ``final parsec problem,'' i.e., how black hole binaries manage to shrink to
separations at which emission of gravity waves becomes efficient. A binary
ejects stars by the gravitational slingshot and carves out a loss cone in the
host galaxy. Continued decay of the binary requires a refilling of the loss
cone. We show that the standard treatment of loss cone refilling, derived for
collisionally relaxed systems like globular clusters, can substantially
underestimate the refilling rates in galactic nuclei. We derive expressions for
non-equilibrium loss-cone dynamics and calculate time scales for the decay of
massive black hole binaries following galaxy mergers, obtaining significantly
higher decay rates than heretofore. Even in the absence of two-body relaxation,
decay of binaries can persist due to repeated ejection of stars returning to
the nucleus on eccentric orbits. We show that this recycling of stars leads to
a gradual, approximately logarithmic dependence of the binary binding energy on
time. We derive an expression for the loss cone refilling induced by the
Brownian motion of a black hole binary. We also show that numerical N-body
experiments are not well suited to probe these mechanisms over long times due
to spurious relaxation.
