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. This title, first published in 2016, has been reissued as an Open Access publication on Cambridge Core.
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. This title, first published in 2016, has been reissued as an Open Access publication on Cambridge Core.
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.
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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