Black-Hole Inspiral Resonances

Flanagan and Hinderer have discovered a resonance phenomenon that ruins the adiabatic evolution of inspiral orbits around Kerr blackholes.   Orbits around Kerr black holes are characterized by a polar and azimuthal frequency, generally these two frequencies are not comeasureable.    This allows one to assume that the orbit completely fills the surface of a torus around the black hole, so one can average the various dissipative terms that cause the inspiral and accurately calculate the gravitational waveform.  However, when these two frequencies near the ratio of two small integers, this ergodic assumption fails and so does the averaging.   If the ratio is of two large integers, the duration of non-ergodicity is short so little phase error accumulates; however, for small integers the error in phase is of order unity.

http://arxiv.org/abs/1009.4923 Transient resonances in the inspirals of point particles into black holes