Testing General Relativity and Informing Astrophysics with Gravitational Waves

In this talk, I present the theoretical models and data analysis tools I developed for testing general relativity and informing astrophysical theories with gravitational-wave observations. First, I present my work on black hole ringdown. I demonstrate that pseudospectral instabilities could affect the quasinormal mode spectrum of black holes, while including rapidly decaying overtone modes in ringdown models could lead to overfitting. To counter this, I develop a frequency-agnostic method for extracting these modes from numerical simulations. I confirm the existence of nonlinear modes in the ringdown and create models connecting mode amplitudes to the initial conditions of the binary black hole merger. Second, I present my work on the effects of gravitational lensing on gravitational waves. I develop software tools to model diffraction-lensing effects due to low-mass dark matter halos, and perform Bayesian parameter inference on the event GW231123, showing that its lensing interpretation depends on prior assumptions. Third, I present my work on searching for black hole mergers with intermediate mass ratios in the third observing run data of LIGO-Virgo-KAGRA, setting bounds on their rate density in the local Universe. Together, these advancements help interface gravitational-wave detections with gravitational physics and astrophysics science goals.