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Birkhäuser

The Einstein Equations and the Large Scale Behavior of Gravitational Fields

50 Years of the Cauchy Problem in General Relativity

  • Conference proceedings
  • © 2004

Overview

Editors:
  1. Piotr T. Chruściel

    1. Laboratoire de Mathématiques et de Physique Théorique, CNRS UMR 6083, Tours, France

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  2. Helmut Friedrich

    1. Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, Golm, Germany

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    You can also search for this editor in PubMed   Google Scholar

  • There exists at present no other book on Einstein's field equations which combines
  • introductory material on the Einstein equations and their analysis
  • a comprehensive, up-to-date survey of the various aspects of the field and its applications
  • an in-depth discussion of the structure and interpretation of their solutions

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Table of contents (13 papers)

  1. Front Matter

    Pages i-xi
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  2. The Constraint Equations

    • Robert Bartnik, Jim Isenberg
    Pages 1-38

  3. The Penrose Inequality

    • Hubert L. Bray, Piotr T. Chruściel
    Pages 39-70

  4. The Global Existence Problem in General Relativity

    • Lars Andersson
    Pages 71-120

  5. Smoothness at Null Infinity and the Structure of Initial Data

    • Helmut Friedrich
    Pages 121-203

  6. Status Quo and Open Problems in the Numerical Construction of Spacetimes

    • Luis Lehner, Oscar Reula
    Pages 205-229

  7. The Einstein-Vlasov System

    • Alan D. Rendall
    Pages 231-250

  8. Future Complete U(1) Symmetric Einsteinian Spacetimes, the Unpolarized Case

    • Yvonne Choquet-Bruhat
    Pages 251-298

  9. Future Complete Vacuum Spacetimes

    • Lars Andersson, Vincent Moncrief
    Pages 299-330

  10. The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic

    • John L. Friedman
    Pages 331-346

  11. Cheeger-Gromov Theory and Applications to General Relativity

    • Michael T. Anderson
    Pages 347-377

  12. Null Geometry and the Einstein Equations

    • Gregory J. Galloway
    Pages 379-400

  13. Group Actions on Lorentz Spaces, Mathematical Aspects: A Survey

    • Thierry Barbot, Abdelghani Zeghib
    Pages 401-439

  14. Gauge, Diffeomorphisms, Initial-Value Formulation, Etc.

    • Robert Geroch
    Pages 441-477

  15. Back Matter

    Pages 479-481
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Keywords

About this book

The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out.

Background material on techniques in PDE theory, differential geometry, and causal theory is provided.

Editors and Affiliations

  • Laboratoire de Mathématiques et de Physique Théorique, CNRS UMR 6083, Tours, France

    Piotr T. Chruściel

  • Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, Golm, Germany

    Helmut Friedrich

Bibliographic Information

  • Book Title: The Einstein Equations and the Large Scale Behavior of Gravitational Fields

  • Book Subtitle: 50 Years of the Cauchy Problem in General Relativity

  • Editors: Piotr T. Chruściel, Helmut Friedrich

  • DOI: https://doi.org/10.1007/978-3-0348-7953-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2004

  • Hardcover ISBN: 978-3-7643-7130-2Published: 27 September 2004

  • Softcover ISBN: 978-3-0348-9634-4Published: 23 October 2012

  • eBook ISBN: 978-3-0348-7953-8Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XI, 485

  • Topics: Classical and Quantum Gravitation, Relativity Theory, Mathematical Methods in Physics

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