Symmetries of Cauchy Horizons and Global Stability of Cosmological Models

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Authors

Luo, Xianghui, 1983-

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University of Oregon

Abstract

This dissertation contains the results obtained from a study of two subjects in mathematical general relativity. The first part of this dissertation is about the existence of Killing symmetries in spacetimes containing a compact Cauchy horizon. We prove the existence of a nontrivial Killing symmetry in a large class of analytic cosmological spacetimes with a compact Cauchy horizon for any spacetime dimension. In doing so, we also remove the restrictive analyticity condition and obtain a generalization to the smooth case. The second part of the dissertation presents our results on the global stability problem for a class of cosmological models. We investigate the power law inflating cosmological models in the presence of electromagnetic fields. A stability result for such cosmological spacetimes is proved. This dissertation includes unpublished co-authored material.

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ix, 111 p.

Keywords

Theoretical physics, Mathematics, Applied mathematics, Cauchy horizon, Cosmology, General relativity, Global stability, Hyperbolic partial differential equations, Mathematical relativity

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