Conformal Methods in General Relativity (Cambridge Monographs on Mathematical Physics)
Cambridge University Press
Edition: Illustrated, 7/21/2016
EAN 9781107033894, ISBN10: 1107033896
Hardcover, 622 pages, 25.4 x 18 x 4.1 cm
Language: English
Originally published in English
This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.
List of symbols
Preface
1. Introduction
Part I. Geometric Tools
2. Differential Geometry
3. Spacetime spinors
4. Space spinors
5. Conformal Geometry
Part II. General Relativity and Conformal Geometry
6. Conformal extensions of exact solutions
7. Asymptotic simplicity
8. The conformal Einstein field equations
9. Matter models
10. Asymptotics
Part III. Methods of PDE Theory
11. The conformal constraint equations
12. Methods of the theory of hyperbolic differential equations
13. Hyperbolic reductions
14. Causality and the Cauchy problem in General Relativity
Part IV. Applications
15. De Sitter-like spacetimes
16. Minkowski-like spacetimes
17. Anti-de Sitter-like spacetimes
18. Characteristic problems for the conformal field equations
19. Static solutions
20. Spatial infinity
21. Perspectives
References
Index.