PhD Candidate 

Michael LaHaye

Abstract

The topic of this thesis is the modelling of gravitational waves for perturbed black holes, and consists of three manuscripts. To do this, we work mainly within two relevant regimes that allows for semi-analytic waveform models: the post-Newtonian approximation and the extreme mass-ratio approximation. The first represents current waveform modelling for current generation, ground-based, gravitational wave detectors like the Laser Interferometer Ground Observatory (LIGO), and the second represents waveform modelling for next generation, space-based, gravitational wave detectors like the Laser Interferometer Space Antenna (LISA).
The first manuscript is a follow up to a previous work on the computation of the static self-force, an important aspect of the perturbation theory of fields in curved spacetime, relevant to the computation of gravitational waves. The previous work employs a new method of computing the static self-force: cosmic strings [1]. Here we seek to answer the remaining questions of why the strings in the previous work were forced to be massless, and can we force them to be massive. We show that it is indeed possible, and illustrate the resulting spacetimes.

In the second manuscript we develop a method of rapidly evaluating the precession dynamics of orbiting bodies whose spin-induced quadrupole moments are different from those of black holes. The modified precession dynamics can then in turn be used to compute a modified waveform model that can be used to probe differences in the spin-induced quadrupole moment of compact bodies for deviations from their value in general relativity (GR). As we will show, this potentially allows one to search for deviations from GR or black hole mimickers with current generation gravitational wave (GW) detectors.

In the final manuscript we develop a framework for computing the modifications to the GWs emitted from extreme- mass ratio inspirals (EMRIs) in a perturbed Schwarzschild geometry. This framework relies on the modified Teukolsky framework developed in [2], with appropriate source terms for an EMRI now included. This work represents the first step towards computing the modifications to the GW signal for more astrophysically relevant scenarios, and will allow us to probe these deviations with GW detectors in the future.

Examination Committee

• Dr. Martin Williams, Chair
• Dr. Eric Poisson, Advisor
• Dr. Huan Yang, Advisory Committee
• Dr. Niayesh Afshordi, Graduate Faculty
• Dr. Michael Kesden, External Examiner (University of Texas at Dallas)