UBC Theses and Dissertations
Dimensional reduction and spacetime pathologies Slobodov, Sergei
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 topological rigidity 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 timelike curves generically appearing in general relativity are a mathematical artifact of periodic coordinate identiﬁcations, using, in part, the dimensional reduction 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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