Black holes in modified theories of gravity

In recent years there has been huge interest in understanding whether Einstein's theory of General Relativity is the correct description of gravity in our universe. The mysterious required presence of dark energy and dark matter has made it plausible that Einstein's original theory may not be the correct one beyond describing solar system behaviour.
The recent experimental observations of gravitational waves provide a remarkable new window into the behaviour of spacetime in the strong gravitational regime. While the first experimental results broadly agree with Einstein's original theory, future generations of such experiments will allow this strong field regime to be probed with much greater precision in the next couple of decades. An important question is; if gravity isn't described by General Relativity, but a modified theory of gravity, what do black holes look like, and how do they behave? However in general little is know about even the simplest non-rotating black holes in modified theories of gravity, and certainly not rotating ones or their dynamics. This is because understanding these typically requires novel numerical calculations involving the complicated Einstein equations. This thesis will focus on combining analytical understanding with novel numerical approaches to solve these problems, with a view to informing the comparison of experiment with theory. A specific goal will be to develop novel numerical methods to allow the study of gravitational collapse in the `massive gravity' modification of Einstein's theory (the `dRGT massive gravity theory'). This is a very basic modification of Einstein's theory, and black holes have complicated behaviour in it. It is a well motivated and fundamental modification, and has attracted huge attention. Despite this, very little is known about whether black holes can form and what they might look like. Here we will address this by solving the novel dynamics numerically, firstly for spherically symmetric collapse of scalar field matter. Beyond this, we will look at the rotating case of collapse, and black holes and their formation in other well motivated modified theories.