The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years Of The Cauchy Problem In General Relativity

by Chrusciel, Piotr T.

• ISBN13: 9783764371302
• ISBN10: 3764371307
• Edition: DVD
• Format: Hardcover
• Copyright: 2004-11-30
• Publisher: Springer Verlag

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.

Table of Contents

Preface	vii
R. Bartnik and J. Isenberg
The Constraint Equations	1	(38)
H.L. Bray and P.T. Chrusciel
The Penrose Inequality	39	(32)
L. Andersson
The Global Existence Problem in General Relativity	71	(50)
H. Friedrich
Smoothness at Null Infinity and the Structure of Initial Data	121	(84)
L. Lehner and O. Reula
Status Quo and Open Problems in the Numerical Construction of Spacetimes	205	(26)
A.D. Rendall
The Einstein-Vlasov System	231	(20)
Y. Choquet-Bruhat
Future Complete U(1) Symmetric Einsteinian Spacetimes, the Unpolarized Case	251	(48)
L. Andersson and V. Moncrief
Future Complete Vacuum Spacetimes	299	(32)
J.L. Friedman
The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic	331	(16)
M.T. Anderson
Cheeger-Gromov Theory and Applications to General Relativity	347	(32)
G.J. Galloway
Null Geometry and the Einstein Equations	379	(22)
T. Barbot and A. Zeghib
Group Actions on Lorentz Spaces, Mathematical Aspects: A Survey	401	(40)
R. Geroch
Gauge, Diffeomorphisms, Initial-Value Formulation, Etc	441	(38)
Index	479