Description
Book SynopsisThe aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singul
Trade ReviewWinner of the 1999 Bocher Memorial Prize, American Mathematical Association "This book presents the authors' theorem on the stability of Minkowski space, a landmark in the development of mathematical relativity. The book is quite self-contained... The book is not easy to read, due to the very technical nature of its contents, but under the circumstances the quality of the exposition is excellent."--Mathematical Reviews
Table of ContentsAcknowledgments1Introduction1IPreliminary Results in 2-and 3-Dimensional Riemannian Geometry2Generalized Hodge Systems in 2-D313General Results in 3-D Geometry534The Poisson Equation in 3-D785Curvature of an Initial Data Set1106Deformation of 2-Surfaces in 3-D121IIBianchi Equations in Space-Time7The Comparison Theorem1358The Error Estimates205IIIConstruction of Global Space-Times. Proof of the Main Theorem9Construction of the Optical Function26110Third Version of the Main Theorem28411Second Fundamental Form31112The Lapse Function34113Derivatives of the Optical Function35114The Last Slice41115The Matching44316The Rotation Vectorfields46617Conclusions491Bibliography513
