The Global Nonlinear Stability of the Minkowski Space (PMS-41) / Sergiu Klainerman, Demetrios Christodoulou.

Format:

Book

Author/Creator:

Christodoulou, Demetrios, 1951- author.

Klainerman, Sergiu, author.

Series:

Princeton Legacy Library

Princeton Mathematical Series ; 153

Language:

English

Subjects (All):

Space and time--Mathematics.

Space and time.

Generalized spaces.

Nonlinear theories.

Physical Description:

1 online resource (525 p.)

Edition:

Course Book

Place of Publication:

Princeton, NJ : Princeton University Press, [2014]

Language Note:

English

Summary:

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.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Contents:

Frontmatter

Table of Contents

Acknowledgments

CHAPTER 1. Introduction

Part I. Preliminary Results in 2- and 3-Dimensional Riemannian Geometry

CHAPTER 2. Generalized Hodge Systems in 2-D

CHAPTER 3. General Results in 3-D Geometry

CHAPTER 4. The Poisson Equation in 3-D

CHAPTER 5. Curvature of an Initial Data Set

CHAPTER 6. Deformation of 2-Surfaces in 3-D

Part II. Bianchi Equations in Space-Time

CHAPTER 7. The Comparison Theorem

CHAPTER 8. The Error Estimates

Part III. Construction of Global Space- Times. Proof of the Main Theorem

CHAPTER 9. Construction of the Optical Function

CHAPTER 10. Third Version of the Main Theorem

CHAPTER 11. Second Fundamental Form

CHAPTER 12. The Lapse Function

CHAPTER 13. Derivatives of the Optical Function

CHAPTER 14. The Last Slice

CHAPTER 15. The Matching

CHAPTER 16. The Rotation Vectorfields

CHAPTER 17. Conclusions

Bibliography

Notes:

Description based upon print version of record.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9780691632551

0691632553

9781400863174

1400863171

OCLC:

884013021