The Einstein Equations and the Large Scale Behavior of Gravitational Fields - 50 Years of the Cauchy Problem in General Relativity

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.

List of contents

The Constraint Equations.- The Penrose Inequality.- The Global Existence Problem in General Relativity.- Smoothness at Null Infinity and the Structure of Initial Data.- Status Quo and Open Problems in the Numerical Construction of Spacetimes.- The Einstein-Vlasov System.- Future Complete U(1) Symmetric Einsteinian Spacetimes, the Unpolarized Case.- Future Complete Vacuum Spacetimes.- The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic.- Cheeger-Gromov Theory and Applications to General Relativity.- Null Geometry and the Einstein Equations.- Group Actions on Lorentz Spaces, Mathematical Aspects:A Survey.- Gauge, Diffeomorphisms, Initial-Value Formulation, Etc..

Summary

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.

Product details

• Assisted by: Piotr T. Chrusciel (Editor), Friedrich (Editor), Friedrich (Editor), Helmut Friedrich (Editor), Piot T Chrusciel (Editor), Piotr T Chrusciel (Editor)
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 12.08.2013
• EAN: 9783034896344
• ISBN: 978-3-0-3489634-4
• No. of pages: 485
• Dimensions: 155 mm x 235 mm x 30 mm
• Weight: 759 g
• Illustrations: XI, 485 p.
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Gravitation, B, Mathematische Physik, Physics, Solution, Physics and Astronomy, Relativity physics, Mathematical physics, Mathematical Methods in Physics, Classical and Quantum Gravity, Classical and Quantum Gravitation, Relativity Theory, Theory of Relativity, vacuum