Abstract
The primary focus of this thesis lies in understanding binary black hole (BBH) mergers through the prism of computational simulations, approximate modeling, and observation. To simulate gravitational waveforms, we employ two distinct approaches: numerical relativity (NR) and point particle black hole perturbation theory (ppBHPT). While NR excelsin the comparable mass regime, ppBHPT is known to be accurate in the extreme mass ratio limit. We employed these frameworks not only to comprehend the dynamics of the binary but also to unveil the connections between these two frameworks. Our work offers a breakthrough in GW source modeling by establishing a simple yet non-trivial scaling between ppBHPT and NR waveforms (and fluxes) in the comparable mass regime. Building upon this scaling, we construct reduced-order surrogate models for waveforms and key remnant parameters (such as final mass, final spin, and kick velocity) for binaries in both comparable mass and extreme mass ratio regime. Furthermore, we develop first NR surrogate models for eccentric binary black hole systems, which are expected to play an increasingly important role in current and future GW detectors. These surrogates exhibit excellent agreement to the underlying NR and ppBHPT data used in training. Subsequently, we employ these surrogate models in the analysis of real GW events. Specifically, we present an in-depth analysis of the third gravitational wave catalog (GWTC-3) using NR surrogate models for precessing binaries. Our findings demonstrate that these surrogates offer noticeably different measurement of binary source properties (such as the masses and spins) compared to other phenomenological approximants. Through this analysis, we also identify four binaries that generated large recoil velocities. Finally, we present new methods designed to expedite data analysis, facilitating real-time source characterization and localization. To enhance accessibility and foster collaboration, we have made all our results publicly available through open-source packages such as gwsurrogate, BHPTNRSurrogate, EMRISurrogate, BHPTNRRemnant, gw-remnant, gwMRE, and cogwheel. Our datasets are publicly available through Zenodo.