The Einstein Equations and the Large Scale Behavior of Gravitational Fields

This book presents state-of-the-art results on the analysis of the Einstein field equations and the large scale structure of their solutions.
It combines in a unique way introductory chapters and surveys written by distinguished researchers, discusses applications to geometrical studies, points out open problems, and provides background material on techniques in PDE theory, differential geometry, and causal theory.
Graduate students, analysts and numerical relativists will profit from this access to recent research on the analysis and structure of Einstein's equations and the behavior of their solutions.

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.

Inhalt
Preface.- 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.- Future Complete Vacuum Spacetimes .- The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic.- Cheeger-Gromov Theory.- Null Geometry and the Einstein Equations.- Group Actions on Lorentz Spaces.- Gauge, Diffeomorphisms, Initial-Value Formulation.- Index