Conformal Methods in General Relativity / / Juan A. Valiente Kroon.
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 ba...
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| Place / Publishing House: | Cambridge, England : : Cambridge University Press,, 2017. |
| Year of Publication: | 2017 |
| Language: | English |
| Physical Description: | 1 online resource (594 pages) |
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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.