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 \sim 10 ^ { -6 } , 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 .
Resonances effects will increase the computational challenge of accurately modeling these sources .