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Birkhäuser

The Evolution Problem in General Relativity

  • Book
  • © 2003

Overview

Authors:
  1. Sergiu Klainerman

    1. Department of Mathematics, Princeton University, Princeton, USA

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  2. Francesco Nicolò

    1. Dipartimento di Matematica, Facoltà di Scienze, M.F.N., Università degli studi di Roma “Tor Vergata”, Roma, Italy

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Progress in Mathematical Physics (PMP, volume 25)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introdution

    • Sergiu Klainerman, Francesco Nicolò
    Pages 1-29

  3. Analytic Methods in the Study of the Initial Value Problem

    • Sergiu Klainerman, Francesco Nicolò
    Pages 31-54

  4. Definitions and Results

    • Sergiu Klainerman, Francesco Nicolò
    Pages 55-114

  5. Estimates for the Connection Coefficients

    • Sergiu Klainerman, Francesco Nicolò
    Pages 115-202

  6. Estimates for the Riemann Curvature Tensor

    • Sergiu Klainerman, Francesco Nicolò
    Pages 203-240

  7. The Error Estimates

    • Sergiu Klainerman, Francesco Nicolò
    Pages 241-294

  8. The Initial Hypersurface and the Last Slice

    • Sergiu Klainerman, Francesco Nicolò
    Pages 295-346

  9. Conclusions

    • Sergiu Klainerman, Francesco Nicolò
    Pages 347-373

  10. Back Matter

    Pages 375-385
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Keywords

About this book

The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys­ tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem.

Reviews

"The book . . . gives a new proof of the central part of the theorem of Christodoulou and S. Klainerman, The global nonlinear stability of the Minkowski space . . . The authors prove, working in terms of double null foliations, a nonlinear stability, or global existence for small data, result for exterior domains."

—Mathematical Reviews

"...Important results in this book are presented in a more ‘digestible’ form [than] in the preceding book [‘The global nonlinear stability of the Minkowski space’] and thus scientists and graduate students working in relativity are recommended to read at least the introduction and the conclusions."

—Applications Of Mathematics

"...This important monograph, presenting the detailed proof of an important result in general relativity, is of great interest to researchers and graduate students in mathematics, mathematical physics, and physics in the area of general relativity."

—Studia Universitatis Babes-Bolyai, Series Mathematica

"The main purpose of this book is to revisit the global stability of Minkowski space as set out by D. Chrostodoulou and S. Klainerman (1993). Here the authors provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets."

—BookNews 

Authors and Affiliations

  • Department of Mathematics, Princeton University, Princeton, USA

    Sergiu Klainerman

  • Dipartimento di Matematica, Facoltà di Scienze, M.F.N., Università degli studi di Roma “Tor Vergata”, Roma, Italy

    Francesco Nicolò

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