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

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

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    Available in PDF Format | The Cauchy Problem in General Relativity (ESI Lectures in Mathematics and Physics).pdf | Unknown
    Hans Ringstrom
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  
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  • PDF | 307 pages
  • Hans Ringstrom
  • European Mathematical Society
  • Unknown
  • 5
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