The robustness of binary black hole mergers and waveforms

In the past five years, the field of numerical relativity has changed dramatically. With many groups now able to simulate merging black holes and more breakthroughs coming almost monthly, there is much competition to pick off as many astrophysically relevant situations as possible. It is sensible, though, to step back from this competition and to look on the new techniques and results with more skeptical eyes than before.;In this dissertation we look at two aspects of initial data from new perspectives and find the waveforms generated from merging binary black hole (BBH) systems to be robust to significant errors in the initial data. In the first study we find that, by adding tuneable auxiliary gravitational waves into a BBH spacetime, up to 1% extra Arnowitt-Deser-Misner (ADM) energy can be added to a standard BBH system before the waveforms are significantly altered. While this study is based on observations of spurious radiation found in all standard initial data sets to date, the second study takes a more general approach. With an eye towards setting up more complex black hole (BH) systems, we find that evolutions of skeleton approximate initial data based on solutions to the ADM Hamiltonian with point sources also yield robust gravitational waveforms that are accurate enough for use in matched template searches for gravitational wave signals in the Laser Interferometer Gravitational-wave Observatory (LIGO) band. We also consider the interpretation of a possible class of constraint violations as an unphysical negative energy field that is absorbed by the BHs. Both of these studies show that the change in apparent horizon (AH) masses during the evolution is a good way to gauge the robustness of the extracted waveforms.;At the end of this dissertation we discuss ongoing work on evolving BBH mergers embedded in gaseous clouds. This is the first study with the new matter code Scotch which couples a hydrodynamic matter field to the fully-nonlinear spacetime evolution code. Evolving a wet BBH system will gauge how robust gravitational wave templates are given that true astrophysical sources are not in vacuum. This is a first step at considering the larger question of whether the presence of gas can overcome the "last parsec" problem, hastening the mergers and thereby increasing the expected merger rates.