Topics in Gravitational Wave Physics: Black-Hole Spectroscopy, Neutron Star Dynamical Tides, and Numerical Relativity

In this thesis, we explore various topics in gravitational wave physics, including black hole spectroscopy, dynamical tides of neutron stars, numerical relativity, and modified theories of gravity. In our study of black hole spectroscopy, we develop a novel framework for identifying quasinormal modes in ringdown signals. We apply this method to numerical-relativity waveforms of binary black hole systems and find second-order and retrograde quasinormal modes in the ringdown regime. We also apply this method to GW150915, resulting in new insights into the existence of the first overtone. On the other hand, we explore how the excitation of quasinormal modes encodes information about binaries’ parameters. Focusing on superkick configurations, we find universal dependence of the mode amplitudes and phases on the binary’s configurations. Tidal effects have significant imprints on gravitational waves emitted during the final stage of the coalescence of binaries involving neutron stars. We examine how dynamical tides can be significant when neutron stars’ characteristic oscillations become resonant with orbital motion, and we investigate their impact on measuring neutron-star parameters with gravitational waves. Specifically, we conduct systematic studies on the tidal excitation of fundamental and Rossby modes of spinning neutron stars and find that their effects may be significant and detectable in the era of third-generation gravitational-wave detectors, which in turn could lead to more stringent constraints on the properties of neutron stars. Regarding numerical relativity, we implement a fully relativistic three-dimensional Cauchy-characteristic matching algorithm to establish a more accurate boundary condition for numerical-relativity simulations. We justify the correctness of the algorithm by nonlinearly propagating gravitational-wave pluses and find that the new boundary condition does reduce spurious numerical reflection at outer boundaries and improves the accuracy of the generated waveforms. The second part focuses on the initial data of binary black holes for numerical simulations. We extend the superposed harmonic initial data, which breaks down for high-spin black holes, to higher spins by introducing a new spatial coordinate system: superposed modified harmonic. We find that the new initial data preserves a nice property of the superposed harmonic system: the suppression of junk radiation. Furthermore, we find that the volume-weighted constraint violations for the new initial data converge with numerical resolution during the junk stage, which means there are fewer high-frequency components at outer spacetime regions. Finally, we investigate the features of gravitational waves within theories beyond general relativity, focusing on two specific aspects. First, we present a numerical-relativity simulation of a black hole-neutron star merger in scalar-tensor gravity with binary parameters consistent with the gravitational wave event GW200115. We consider the Damour-Esposito-Farèse extension to Brans-Dicke theory and find that the scalar-tensor system evolves faster than its general-relativity counterpart due to dipole radiation, merging a full gravitational-wave cycle before the GR counterpart. We also compare the numerical waveforms with post-Newtonian theory and find good agreement during the inspiral. Second, we propose a new approach, based on numerical-relativity waveforms, for reconstructing the late-time near-horizon geometry of merging binary black holes and computing gravitational-wave echoes from exotic compact objects. We use a physically-motivated way to impose boundary conditions near the horizon and apply the Boltzmann reflectivity to compute the quasinormal modes of non-rotating ECOs, as well as gravitational-wave echoes. Additionally, we investigate the detectability of these echoes in current and future detectors and prospects for parameter estimation.