Presentation Archive

Transient resonances in extreme mass ratio inspirals

Tanja Hinderer

October 18, 2010



Abstract: The two body problem in general relativity, in the highly relativistic, extreme mass-ratio regime for spinning black holes has a qualitatively new feature which is not seen in the weak-field limit: the effects of transient resonances. 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. The effects of resonances make orbits more sensitive to changes in initial data and give rise to corrections to the gravitational wave signal’s phase which 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. Our results apply to an important potential source of gravitational waves, the gradual inspiral of compact objects 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. From numerically evolving fully relativistic orbital dynamics supplemented with an approximate, post-Newtonian self-force, we estimate that the resonance phase shifts will be of order a few tens of cycles for mass ratios $sim 10^{-6}$.