The Cauchy Problem in General Relativity (ESI Lectures in Mathematics and Physics)

Introduction Outline Part I. Background from the theory of partial differential equations: Functional analysis The Fourier transform Sobolev spaces Sobolev embedding Symmetric hyperbolic systems Linear wave equations Local existence, non-linear wave equations Part II. Background in geometry, global hyperbolicity and uniqueness: Basic Lorentz geometry Characterizations of global hyperbolicity Uniqueness of solutions to linear wave equations Part III. General relativity: The constraint equations Local existence Cauchy stability Existence of a maximal globally hyperbolic development Part IV. Pathologies, strong cosmic censorship: Preliminaries Constant mean curvature Initial data Einstein's vacuum equations Closed universe recollapse Asymptotic behaviour LRS Bianchi class A solutions Existence of extensions Existence of inequivalent extensions Appendices Bibliography Index