Transient resonances in the inspirals of point particles into black
  holes
  We show that transient resonances occur in the two body problem in general
relativity, in the highly relativistic, extreme mass-ratio regime for spinning
black holes. These resonances occur when the ratio of polar and radial orbital
frequencies, which is slowly evolving under the influence of gravitational
radiation reaction, passes through a low order rational number. At such points,
the adiabatic approximation to the orbital evolution breaks down, and there is
a brief but order unity correction to the inspiral rate. Corrections to the
gravitational wave signal's phase due to resonance effects scale as the square
root of the inverse of mass of the small body, and thus become large in the
extreme-mass-ratio limit, dominating over all other post-adiabatic effects. The
resonances make orbits more sensitive to changes in initial data (though not
quite chaotic), and are genuine non-perturbative effects that are not seen at
any order in a standard post-Newtonian expansion. Our results apply to an
important potential source of gravitational waves, the gradual inspiral of
white dwarfs, neutron stars, or black holes into much more massive black holes.
It is hoped to exploit observations of these sources to map the spacetime
geometry of black holes. However, such mapping will require accurate models of
binary dynamics, which is a computational challenge whose difficulty is
significantly increased by resonance effects. We estimate that the resonance
phase shifts will be of order a few tens of cycles for mass ratios $\sim
10^{-6}$, by numerically evolving fully relativistic orbital dynamics
supplemented with an approximate, post-Newtonian self-force.
