The global nonlinear stability of the Minkowski space
著者
書誌事項
The global nonlinear stability of the Minkowski space
（Princeton mathematical series, 41）
Princeton University Press, 1993
- : hbk
- : pbk
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注記
Bibliography: p. 513-514
内容説明・目次
- 巻冊次
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: hbk ISBN 9780691087771
内容説明
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 a rigorous derivation of the laws of gravitation proposed by Bondi can be given. 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.
- 巻冊次
-
: pbk ISBN 9780691603155
内容説明
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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目次
Acknowledgments1Introduction1IPreliminary 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
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