The Global Nonlinear Stability of the Minkowski Space (pms-41) (ebook)

Argumento de The Global Nonlinear Stability of the Minkowski Space (pms-41) (ebook)

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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Winner 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 0Acknowledgments 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