Electromagnetic Fields and Radiation in Dynamical Spacetimes

Abstract

In this dissertation, I present the development and application of new mathematical and computational tools to study dynamical spacetimes with extreme gravitational and electromagnetic fields. I discuss and implement a formalism to generate initial data for general relativistic simulations of generic black hole configurations with charge. I introduce techniques to obtain stable quasi-circular inspirals and mergers and I perform the first simulations of this kind. I use these results to place the first constraint on the charge of astrophysical black holes and on specific modified theories of gravity using the gravitational wave event GW150914. I present and benchmark approximate methods to study these systems and derive an analytical technique to estimate the properties of the remnant left by a merger of charged black holes. I investigate ultra-relativistic collisions of charged binaries and discuss their implications for a variety of conjectures in theoretical and fundamental physics. I argue that in the full non-linear theory, neither ultra-relativistic collisions nor quasi-circular inspiral can overcharge a black hole and produce a naked singularity. Finally, I present new software for numerical relativity, including a novel code to perform ray tracing and radiation transfer. I use this code to describe some subtle features of general relativistic ray tracing.