Transient Resonances in the Inspirals of Point Particles into Black Holes

Abstract

We show that transient resonances occur in the two-body problem in general relativity for spinning black holes in close proximity to one another when one black hole is much more massive than the other. 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 resonances cause a perturbation to orbital phase of order a few tens of cycles for mass ratios ∼10(-6), make orbits more sensitive to changes in initial data (though not quite chaotic), and are genuine nonperturbative 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. Resonances' effects will increase the computational challenge of accurately modeling these sources.