Eccentric-orbit binary black hole inspirals: Informing the post-Newtonian expansion through black hole perturbation theory and multipole moment analysis

Abstract

The era of gravitational-wave astronomy has arrived. As a result, we now have the opportunity to observe features of the universe previously hidden from human view. To advance efforts on wave detection, this dissertation presents new results on the dynamics of non-spinning binary black hole (BBH) inspirals. In it I focus on the eccentric-orbit extreme-mass-ratio inspiral (EMRI), a presently underdeveloped class of BBHs in which the orbit has an elliptical shape and one of the two masses is much larger than the other. I investigate these EMRIs by combining two common approaches --- the small-mass-ratio approximation of black hole perturbation theory (BHPT) and the small-velocity approximation of post-Newtonian (PN) theory --- in novel ways to better describe their evolution. BHPT is studied using the Mano-Suzuki-Takasugi formalism to represent first-order perturbations as infinite summations of hypergeometric functions. These solutions are then analyzed in the slow-motion regime to derive high-order PN series for observable quantities, with particular focus on the fluxes: the total energy and angular momentum radiated by the system. BHPT-PN expansions for the fluxes at infinity are found separately using numerical and analytical approaches to compare efficacy. The result is the derivation of flux terms to at least $e^{20}$ through 10PN and at least $e^{10}$ through 19PN. Results to 10PN/$e^{20}$ and 18PN/$e^{10}$ are similarly found for the fluxes at the central horizon. Simultaneously, the fluxes at infinity are studied within PN theory using the multipolar post-Minkowskian PN formalism. By manipulating certain multipole moments in Fourier space, we find infinite sets of previously unknown multipole contributions. Compact forms are derived for the leading logarithm flux terms and their 1PN corrections. Drastic simplifications are made to the subleading logarithms and their 1PN corrections. Compact expressions are extracted for the full 4PN and 6PN Log fluxes at lowest order in the mass ratio. Finally, similar analytical techniques are applied to derive novel BHPT-PN expansions for two local conserved quantities: the generalized redshift invariant and spin-precession invariant. The former is found to 8.5PN and $e^{20}$ and the latter to 6.5PN and $e^{16}$. Overall, this thesis offers a deeper understanding of the gravitational radiation and orbital motion of EMRIs and finds new structure in the BHPT and PN formalisms as a whole. The results contained herein will contribute to the analysis of waveform data obtained by LISA, the space-based gravitational-wave detector scheduled for launch in 2034.