Using perturbation theory to understand the two body problem in general relativity

Abstract

Binary systems composed of compact objects (neutron stars and black holes) radiate gravitational waves (GWs). The prospect of detecting these GWs using ground and space based experiments has made it imperative to understand the dynamics of such compact binaries. This work describes several advances in our ability to model compact binaries and extract the rich science they encode. A major part of this dissertation focuses on the subset of binaries composed of a massive, central black hole (105 - 10SM®) and a much smaller compact object (1 - 100M®). The emission of gravitational energy from such extreme mass ratio inspirals (EMRIs) forces the separation between the two components to shrink, leading to their merger. We treat the smaller object as a point-like particle on the stationary space-time of the larger black hole. The EMRI problem can be broken down into two related parts: (i) A determination of the inspiral trajectory followed by the smaller object, and (ii) A characterization of the gravitational waveforms that result from such an inspiral. The initial part of this work discusses the development of a numerical algorithm that solves for the GWs that result from the perturbations generated by the smaller object. It accepts any reasonable inspiral trajectory as an input and produces the resulting waveforms with an accuracy greater than 99%. Next, we present a technique to model the part of the inspiral trajectory that immediately precedes the final plunge of smaller object into the massive black hole. Along with earlier research, this enables us to compute the smaller object's complete inspiral trajectory.

(cont.) We now have a versatile toolkit that can model GWs from EMRIs. Finally, we present another application of this work. GWs carry linear momentum away from a binary. Integrating the lost momentum leaves an asymmetric binary with a non-zero recoil velocity after merger. We compute the recoils from EMRIs and extrapolate them to comparable mass binaries. We find that extrapolating perturbation theory gives results that agree well with those from numerical relativity, but require far less computation time.