Demetrios Christodoulou & Sergiu Klainerman

Acknowledgments
1 Introduction 1
I Preliminary Results in 2-and 3-Dimensional Riemannian Geometry
2 Generalized Hodge Systems in 2-D 31
3 General Results in 3-D Geometry 53
4 The Poisson Equation in 3-D 78
5 Curvature of an Initial Data Set 110
6 Deformation of 2-Surfaces in 3-D 121
II Bianchi Equations in Space-Time
7 The Comparison Theorem 135
8 The Error Estimates 205
III Construction of Global Space-Times. Proof of the Main Theorem
9 Construction of the Optical Function 261
10 Third Version of the Main Theorem 284
11 Second Fundamental Form 311
12 The Lapse Function 341
13 Derivatives of the Optical Function 351
14 The Last Slice 411
15 The Matching 443
16 The Rotation Vectorfields 466
17 Conclusions 491
Bibliography 513

The 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 singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter.
Originally published in 1994.
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