Ebook: The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity
- Tags: Classical and Quantum Gravitation Relativity Theory, Mathematical Methods in Physics
- Year: 2004
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xi
The Constraint Equations....Pages 1-38
The Penrose Inequality....Pages 39-70
The Global Existence Problem in General Relativity....Pages 71-120
Smoothness at Null Infinity and the Structure of Initial Data....Pages 121-203
Status Quo and Open Problems in the Numerical Construction of Spacetimes....Pages 205-229
The Einstein-Vlasov System....Pages 231-250
Future Complete U(1) Symmetric Einsteinian Spacetimes, the Unpolarized Case....Pages 251-298
Future Complete Vacuum Spacetimes....Pages 299-330
The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic....Pages 331-346
Cheeger-Gromov Theory and Applications to General Relativity....Pages 347-377
Null Geometry and the Einstein Equations....Pages 379-400
Group Actions on Lorentz Spaces, Mathematical Aspects: A Survey....Pages 401-439
Gauge, Diffeomorphisms, Initial-Value Formulation, Etc.....Pages 441-477
Back Matter....Pages 479-481
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.
Content:
Front Matter....Pages i-xi
The Constraint Equations....Pages 1-38
The Penrose Inequality....Pages 39-70
The Global Existence Problem in General Relativity....Pages 71-120
Smoothness at Null Infinity and the Structure of Initial Data....Pages 121-203
Status Quo and Open Problems in the Numerical Construction of Spacetimes....Pages 205-229
The Einstein-Vlasov System....Pages 231-250
Future Complete U(1) Symmetric Einsteinian Spacetimes, the Unpolarized Case....Pages 251-298
Future Complete Vacuum Spacetimes....Pages 299-330
The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic....Pages 331-346
Cheeger-Gromov Theory and Applications to General Relativity....Pages 347-377
Null Geometry and the Einstein Equations....Pages 379-400
Group Actions on Lorentz Spaces, Mathematical Aspects: A Survey....Pages 401-439
Gauge, Diffeomorphisms, Initial-Value Formulation, Etc.....Pages 441-477
Back Matter....Pages 479-481
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