Novel Techniques for Simulation and Analysis of Black Hole Mergers

This dissertation consists of three research topics from numerical relativity: waveforms from inspiral mergers of black hole binaries, recoils from head-on mergers of black holes, and a new computational technique for error-reduction. The first two topics present research from journal articles that I coauthored with my colleagues in the NASA Goddard Numerical Relativity research group. Chapter 2 discusses a heuristic model of black hole binary mergers and the waveforms produced by them, based on simulations of nonspinning black holes. The gravitational radiation is interpreted as the result of an implicit rotating source that generates the radiation modes as the source multipoles rotate coherently. This interpretation of the waveform phase evolution provides a unified physical picture of the inspiral, plunge, and ringdown of the binaries, and it is the basis of an analytic model of the late-time frequency evolution. Chapter 3 presents a study of kicks in head-on black hole mergers, emphasizing the distinct contributions of spin and mass ratio, as well as their combined effects, to these radiation-induced recoils. The simpler dynamics of head-on mergers allow a more clear separation of the two types of kick and a validation of post-Newtonian predictions for the spin scaling of kicks. Finally, Chapter 4 presents a technique I developed to improve the accuracy of the field evolution in numerical relativity simulations. This "moving patches" technique uses local coordinate frames to minimize black hole motion and reduce error due to advection terms. In tests of the technique, I demonstrate reduction in constraint violations and in errors in the orbital frequency derived from the black holes' motions. I also demonstrate an accuracy gain in a new diagnostic quantity based on orbital angular momentum. I developed this diagnostic for evaluating the moving patches technique, but it has broader applicability. Though the moving patches technique has significant performance costs, these limitations are specific to the current implementation, and it promises greater efficiency and accuracy in the future