Conformal Methods in General Relativity
- Author: Juan A. Valiente Kroon, Queen Mary University of London
- Date Published: February 2023
- availability: Available
- format: Hardback
- isbn: 9781009291347
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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 an ideal reference companion on the topic. This title, first published in 2016, has been reissued as an Open Access publication on Cambridge Core.
Read more- Includes over seventy figures and diagrams to illustrate difficult concepts
- Extensive lists of further reading provide the reader with access into the important literature of the subject
- Encourages researchers in related areas to make use of the ideas discussed in their own research
- This title has been reissued as an Open Access publication on Cambridge Core
Reviews & endorsements
'The work serves as an excellent reference on conformal methods for advanced students and researchers. … the text is written well, thoroughly researched, and self-contained.' A. Spero, Choice
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×Product details
- Date Published: February 2023
- format: Hardback
- isbn: 9781009291347
- length: 622 pages
- dimensions: 250 x 175 x 37 mm
- weight: 1.23kg
- availability: Available
Table of Contents
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.
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