Gravitational waves from black hole binaries in the point-particle limit

In this thesis we have developed a new numerical waveform generation algorithm for particle perturbations of rotating black hole spacetimes. The Teukolsky equation, describing the evolution of gravitational perturbations around such black holes, is rederived in horizon-penetrating and hyperboloidal coordinates using a rotated null-tetrad. By comparison with state-of-the-art literature results we prove that the reformulated equation is solvable numerically in the time-domain at excellent accuracy using standard numerical techniques. In this context it improves on the traditional time-domain Teukolsky algorithm presented by Krivan et al. in 1997, and should thus be viewed as the algorithm of choice for future researchers aiming at the numerical solution of the Teukolsky equation in the time domain. After severe sanity checks, the implementation of the algorithm, the teukode, is employed to study several aspects of the black hole binary problem in the particle limit; a multipolar analysis of merger waveforms, consistency checks of the radiation reaction, horizon absorbed gravitational wave fluxes during particle inspirals, kick and antikick velocties, and gravitational waves from spinning particles.