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The Cauchy Problem in General Relativity

Hans Ringström
Publisher: 
European Mathematical Society
Publication Date: 
2009
Number of Pages: 
294
Format: 
Paperback
Series: 
ESI Lectures in Mathematics and Physics
Price: 
58.00
ISBN: 
9783037190531
Category: 
Monograph
We do not plan to review this book.
  • 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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