Conformal Methods in General Relativity

Juan A. Valiente Kroon (Queen Mary University of London)

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English

Cambridge University Press
09 February 2023

Gravity; Relativity physics; Mathematical physics

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.

By: Juan A. Valiente Kroon (Queen Mary University of London)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: Revised edition
Dimensions: Height: 244mm, Width: 170mm, Spine: 31mm
Weight: 1.090kg
ISBN: 9781009291330
ISBN 10: 1009291335
Pages: 622
Publication Date: 09 February 2023
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

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.

Reviews for Conformal Methods in General Relativity

'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