Numerical and analytical models of self-force effects in Kerr extreme-mass-ratio inspirals

Ground-based detectors now regularly observe the merger of stellar-mass compact objects and their gravitational waves. Building on this success, ESA, in partnership with NASA, will launch the space-based LISA observatory to detect milli-Hertz gravitational wave signals. Extreme-mass-ratio inspirals (EMRIs)---binaries composed of a stellar-mass compact object orbiting a massive black hole---are ideal gravitational wave sources for LISA. Because of their unique properties, EMRIs can provide new insights concerning the growth of massive black holes (and their host galaxies) and enable the most precise tests of general relativity. To achieve this science, LISA will rely on accurate EMRI models to search for and analyze gravitational wave signals. The most accurate EMRI models rely on a mechanism known as the gravitational self-force to calculate an EMRI inspiral and the resulting gravitational waveform. For EMRIs with rotating (Kerr) massive black holes, current gravitational self-force calculations are too computationally demanding to be incorporated into full EMRI models. For my dissertation, I built a developmental scalar self-force code to devise and implement new numerical and analytical techniques for calculating self-force effects in Kerr spacetime. I introduce spectral techniques for numerically evaluating Kerr geodesics and the sources of scalar perturbations. I discuss how these methods can be extended to gravitational self-force calculations. With this code, I produced the first calculations of the scalar self-force along resonant and non-resonant inclined, eccentric orbits in Kerr spacetime. With these new resonant calculations I provided one of the first tests of the integrability conjecture, which holds for these scalar self-force results. I also uncovered the existence of a physical effect in EMRI waveforms, now referred to as quasinormal bursts. Quasinormal bursts are periodic high-frequency oscillations in EMRI waveforms which may aid in the characterization of EMRI gravitational wave sources.Doctor of Philosoph