Gravitational Wave Exotica - Advancing the Search for Signatures of Exotic Compact Objects and Gravitational Lensing from Data-Analysis and Theoretical Perspectives

In this thesis, I explore two new arenas of gravitational-wave physics and advance them from both data-analysis and theoretical perspectives. I probe the nature of the remnant of a compact binary merger and study the strong gravitational lensing of gravitational waves. For probing the nature of a merger remnant, I first describe recipes of computing radiation emitted by a perturbed Kerr black hole, and in particular using the Generalized Sasaki-Nakamura formalism. Using a modified Kerr black hole spacetime as a model of a generic compact object, I then describe a prescription to compute waveforms of the repeating bursts of gravitational waves, referred to as gravitational-wave echoes, that are theorized to be emitted when a compact object with a reflective surface is formed as the remnant of a merger. Equipped with a waveform model for these echoes, I present a Bayesian model selection approach to look for echoes in data while inferring properties of the potential exotic compact object. I apply this approach to search for echoes in the data covering the first, the second, and the first half of the third observing run of the LIGO-Virgo-KAGRA network. For the strong lensing of gravitational waves, I first develop a Bayesian statistical framework that is capable of computing the probability of a given set of gravitational-wave events being the strongly-lensed counterparts of the same source or simply coming from distinct sources. If they are truly lensed, the framework can also infer the properties of the lensed source in a way unaffected by lensing. I apply this framework to search for signatures of strongly-lensed binary black hole systems in the data covering the third observing run. While we did not find any statistically significant evidence in the search for gravitational-wave echoes and strongly-lensed binary black holes, we can still place limits using the null results. Admittedly the existence of exotic compact objects is speculative and the observing rate of strongly-lensed gravitational waves is rare; however, the scientific impacts that they can bring are profound if they are proven to exist