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

• Superior document: Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1980-1999
• VerfasserIn: Christodoulou, Demetrios,; Klainerman, Sergiu,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2014]; ©1994
• Year of Publication: 2014
• Edition: Course Book
• Language: English
• Series: Princeton Mathematical Series ; 153
• Physical Description: 1 online resource (526 p.)

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.

Table of 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