Kristin Schleich

Recently, models of spacetime with extra dimensions has driven interest into higher dimensional black holes. In this thesis, we examine general relativity in spacetimes that are not four dimensional. The thesis is divided into three parts. The first part focuses on the higher dimensional Kerr-de Sitter metrics; we examine the separation of variables for the Hamilton-Jacobi and Klein-Gordon equations that occurs for particles and fields in those metrics. In the second part we consider lower dimensional geons, and give a proof that there cannot be any asymptotically flat geons in a three dimensional spacetime. Finally, we examine charged higher dimensional black holes, and consider the possibility of a higher dimensional generalization of the Kerr-Newman metric. We examine some approaches to find that solution, and demonstrate the form that the electromagnetic potential must have in such a spacetime.

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Dimensional reduction is a well known technique in general relativity. It has been used to resolve certain singularities, to generate new solutions, and to reduce the computational complexity of numerical evolution. These advantages, however, often prove costly, as the reduced spacetime may have various pathologies, such as singularities, poor asymptotics, negative energy, and even superluminal matter flows. The first two parts of this thesis investigate when and how these pathologies arise.After considering several simple examples, we first prove, using perturbative techniques, that under certain reasonable assumptions any asymptotically flat reduction of an asymptotically flat spacetime results in negative energy seen by timelike observers. The next part describes the topologicalrigidity theorem and its consequences for certain reductions to three dimensions, confirming and generalizing the results of the perturbative approach. The last part of the thesis is an investigation of the claim that closed timelikecurves generically appearing in general relativity are a mathematical artifact of periodic coordinate identifications, using, in part, the dimensionalreduction techniques. We show that removing these periodic identifications results in naked quasi-regular singularities and is not even guaranteed to get rid of the closed timelike curves.

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