Current experiments hope to detect gravitational waves--oscillations of space and time predicted by Einstein. The strongest sources of gravitational waves are compact object binaries--orbiting neutron stars or black holes. Gravitational waves carry away energy, linear momentum, and angular momentum until the binary merges to form a single black hole. This thesis concerns three distinct projects regarding binary coalescence.

The linear momentum radiated when binaries merge imparts a recoil or "kick" to the final black hole. Black hole recoils have important astrophysical consequences: black holes can be displaced or ejected from their host galaxies or globular clusters, affecting black hole growth, quasar activity, and the density structure of galaxies. We compute the kick velocity using black hole perturbation theory, treating the binary as a small mass spiraling into a massive, spinning black hole. We find that the recoil can easily reach ~100-200 km/s but probably does not exceed 500 km/s.

Binary neutron stars are another important source of gravitational waves. Understanding the final coalescence phase of the gravitational wave signal requires computer simulations. Some numerical simulations have shown that the neutron stars are subject to a crushing force late in the inspiral. This crushing effect has had no explanation and is disputed. We show that a compressive force arises due to a coupling of gravitomagnetic tidal fields to the current-quadrupole moment of the neutron star. However, except in special circumstances, this gravitomagnetic crushing effect is overwhelmed by stabilizing Newtonian tidal interactions.

A small compact object orbiting a massive black hole will be a strong source for space-based gravitational wave detectors. Accurate waveforms for these systems will require computing the self-force on the compact object. The tools to do this do not yet exist. But when the inspiral time is much longer than the orbital period (the adiabatic approximation), approximate waveforms for generic orbits can be computed. We estimate the error in the adiabatic approximation by computing the gravitational wave phase using post-Newtonian theory. We find that, for orbits with small eccentricity, the adiabatic waveforms will be good enough for detection but not for parameter extraction.