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Conformal methods in general relativity / Juan A. Valiente Kroon.

By: Material type: TextTextSeries: Cambridge monographs on mathematical physicsPublication details: Cambridge : Cambridge University Press, 2016.Description: xxx, 594 pages : illustrations ; 26 cmISBN:
  • 9781107033894 (hardback ; alk. paper)
Subject(s): DDC classification:
  • 530.11 23 V172
Contents:
1. Introduction -- 2. Differential geometry -- 3. Spacetime spinors -- 4. Space spinors -- 5. Conformal geometry -- 6. Conformal extensions of exact solutions -- 7. Asymptotic simplicity -- 8. The conformal Einstein field equations -- 9. Matter models -- 10. Asymptotics -- 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 -- 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.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 530.11 V172 (Browse shelf(Opens below)) Available 138043
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Differential geometry --
3. Spacetime spinors --
4. Space spinors --
5. Conformal geometry --
6. Conformal extensions of exact solutions --
7. Asymptotic simplicity --
8. The conformal Einstein field equations --
9. Matter models --
10. Asymptotics --
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 --
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.

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.

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