Research Catalog

Title

The evolution problem in general relativity / Sergiu Klainerman, Francesco Nicolò.

Author

Klainerman, Sergiu, 1950-

Publication

Boston : Birkhäuser, [2003], ©2003.

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Holdings

Details

Additional Authors

Nicolò, Francesco, 1943-

Description

xii, 385 pages; 25 cm.

Summary

• "The global aspects of the problem of evolution equations in general relativity are examined. Central to the work is a revisit of the proof of the global stability of Minkowski space, as presented by Christodoulou and Klainerman (1993). The focus, therefore, is on 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 asymptotic flat initial data sets.
• While technical motivation is clearly and systematically provided for this proof, many important related concepts and results, some well established, others new, unfold along the way." "A comprehensive bibliography and index complete this important monograph, aimed at researchers and graduate students in mathematics, mathematical physics, and physics in the area of general relativity."--BOOK JACKET.

Series Statement

Progress in mathematical physics ; v. 25

Uniform Title

Progress in mathematical physics ; v. 25.

Subject

• General relativity (Physics)
• Evolution equations
• Mathematical physics

Bibliography (note)

• Includes bibliographical references (p. [375]-379) and index.

Contents

• 1. Introduction -- 1.1. Generalities about Lorentz manifolds -- 1.2. The Einstein equations -- 1.3. Local existence for Einstein's vacuum equations -- 2. Analytic Methods in the Study of the Initial Value Problem -- 2.1. Local and global existence for systems of nonlinear wave equations -- 2.2. Weyl fields and Bianchi equations in Minkowski spacetime -- 2.3. Global nonlinear stability of Minkowski spacetime -- 2.4. Structure of the work -- 3. Definitions and Results -- 3.1. Connection coefficients -- 3.2. Bianchi equations in an Einstein vacuum spacetime -- 3.3. Canonical double null foliation of the spacetime -- 3.4. Deformation tensors -- 3.5. The definitions of the fundamental norms -- 3.6. The initial data -- 3.7. The Main Theorem -- 4. Estimates for the Connection Coefficients -- 4.1. Preliminary results -- 4.2. Proof of Theorem M1 --
• 4.3. Proof of Theorem 4.2.1 and estimates for the zero and first derivatives of the connection coefficients -- 4.4. Proof of Theorem 4.2.2 and estimates for the second derivatives of the connection coefficients -- 4.5. Proof of Theorem 4.2.3 and control of third derivatives of the connection coefficients -- 4.6. Rotation tensor estimates -- 4.7. Proof of Theorem M2 and estimates for the D norms of the rotation deformation tensors -- 5. Estimates for the Riemann Curvature Tensor -- 5.1. Preliminary tools -- 6. The Error Estimates -- 6.1. Definitions and prerequisites -- 6.2. The error terms [epsilon][subscript 1] -- 6.3. The error terms [epsilon][subscript 2] -- 7. The Initial Hypersurface and the Last Slice -- 7.1. Initial hypersurface foliations -- 7.2. The initial hypersurface connection estimates -- 7.3. The last slice foliation -- 7.4. The last slice connection estimates -- 7.5. The last slice rotation deformation estimates --
• 7.6. The extension argument -- 8. Conclusions -- 8.1. The spacetime null infinity -- 8.2. The behavior of the curvature tensor at the null-outgoing infinity -- 8.3. The behavior of the connection coefficients at the null-outgoing infinity -- 8.4. The null-outgoing infinity limit of the structure equations -- 8.5. The Bondi mass -- 8.6. Asymptotic behavior of null-outgoing hypersurfaces.

ISBN

• 0817642544 (alk. paper)
• 3764342544 (alk. paper)

LCCN

2002074351

OCLC

• ocm49873259
• SCSB-4327346

Owning Institutions

Columbia University Libraries