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Conformal Methods in General Relativity

$125.00 (C)

  • Date Published: October 2016
  • availability: In stock
  • format: Hardback
  • isbn: 9781107033894

$ 125.00 (C)
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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 the perfect reference companion on the topic.

    • Includes over 70 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
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    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: October 2016
    • format: Hardback
    • isbn: 9781107033894
    • length: 622 pages
    • dimensions: 253 x 181 x 40 mm
    • weight: 1.27kg
    • contains: 73 b/w illus.
    • availability: In stock
  • 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.

  • Author

    Juan A. Valiente Kroon, Queen Mary University of London
    Juan A. Valiente Kroon is a Reader in Applied Mathematics at Queen Mary University of London. He has been a Lise Meitner Fellow of the Austrian FWF and an EPSRC Advanced Research Fellow, and he specialises in various aspects of mathematical general relativity.

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