Quasi-Local Approaches to Black Hole Horizons and Rindler Trajectories in Dynamical Black Hole Spacetimes
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Many introductory texts on general relativity introduce event horizons as the defining feature of black holes. However such seemingly benign constructs have some key physical limitations. Therefore, it is imperative to construct horizons which accurately describe the black hole region in spacetime and that can be used to extract physical properties and not act as merely well defined mathematical constructs. In this thesis we shall discuss the event horizon and its shortcomings. We also review the laws of black hole mechanics and 'quasi-local' horizons that may be seen as alternatives to the event horizon. The laws of black hole mechanics in quasi-local horizons shall be examined. We also present numerical simulations of linear uniformly accelerated trajectories and find the corresponding Rindler horizons in Schwarzschild and Vaidya spacetimes. This thesis will attempt to persuade the reader that event horizons are a useful but limited way to understand the black hole region and that the quasi-local models can offer an elegant and physically insightful alternative. We also derive acceleration bounds for linear uniformly accelerated trajectories in Schwarzschild and Vaidya spacetimes.