Orbital resonances in small mass ratio binaries The two body problem in general relativity, for spinning black holes in close proximity to one another and when one black hole is much more massive than the other, has an intriguing feature: transient resonances. These resonances occur when the ratio of meridional 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 that scales as the square root of the inverse of the small mass ratio, 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 weak-field expansion. This applies 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. Resonance effects will increase the computational challenge of accurately modeling these sources.
>> Read the arXiv version of the paper published in PRL here
>> Read more about a new efficient method to determine the parameter space where the resonances occur and their broader astrophysical implications here and in the longer version here
We discovered the resonances when developing a systematic two-timescale formalism for the two-body problem in the highly relativistic, small mass ratio regime. Such methods are necessary if we want to model the system over a long inspiral time. You can read more about this framework for the orbital motion here.