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Exact Solutions of Einstein's Field Equations

2nd Edition

Part of Cambridge Monographs on Mathematical Physics

  • Date Published: September 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521467025

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  • A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

    • An updated and expanded edition of a classic text, containing important new methods and solutions
    • Includes generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions
    • A unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources
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    Reviews & endorsements

    '… not only is the book an unrivalled source of knowledge on what has been charted of the rugged landscape of curved space-times, but, additionally, it is a well-organized and concise reference in matters of differential geometry.' General Relativity and Gravitation

    '… a remarkable work, and indispensable to any serious practitioner of classical general relativity.' Mathematics Today

    '… will be a lighthouse for those navigating in the ever expanding ocean of exact solutions to Einstein's equations.' Zentralblatt MATH

    'This is clearly a most valuable reference book. It comprehensively reviews known local solutions of Einstein's equation and provides a secure base for future research.' Mathematical Reviews

    'We should be thankful to the authors for having undertaken this project. The second edition, like the first one, is a real masterpiece.' CERN Courier

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    Product details

    • Edition: 2nd Edition
    • Date Published: September 2009
    • format: Paperback
    • isbn: 9780521467025
    • length: 732 pages
    • dimensions: 244 x 175 x 43 mm
    • weight: 1.2kg
    • contains: 10 b/w illus. 50 tables
    • availability: Available
  • Table of Contents

    Preface
    List of tables
    Notation
    1. Introduction
    Part I. General Methods:
    2. Differential geometry without a metric
    3. Some topics in Riemannian geometry
    4. The Petrov classification
    5. Classification of the Ricci tensor and the energy-movement tensor
    6. Vector fields
    7. The Newman–Penrose and related formalisms
    8. Continuous groups of transformations
    isometry and homothety groups
    9. Invariants and the characterization of geometrics
    10. Generation techniques
    Part II. Solutions with Groups of Motions:
    11. Classification of solutions with isometries or homotheties
    12. Homogeneous space-times
    13. Hypersurface-homogeneous space-times
    14. Spatially-homogeneous perfect fluid cosmologies
    15. Groups G3 on non-null orbits V2. Spherical and plane symmetry
    16. Spherically-symmetric perfect fluid solutions
    17. Groups G2 and G1 on non-null orbits
    18. Stationary gravitational fields
    19. Stationary axisymmetric fields: basic concepts and field equations
    20. Stationary axisymmetiric vacuum solutions
    21. Non-empty stationary axisymmetric solutions
    22. Groups G2I on spacelike orbits: cylindrical symmetry
    23. Inhomogeneous perfect fluid solutions with symmetry
    24. Groups on null orbits. Plane waves
    25. Collision of plane waves
    Part III. Algebraically Special Solutions:
    26. The various classes of algebraically special solutions. Some algebraically general solutions
    27. The line element for metrics with κ=σ=0=R11=R14=R44, Θ+iω≠0
    28. Robinson–Trautman solutions
    29. Twisting vacuum solutions
    30. Twisting Einstein–Maxwell and pure radiation fields
    31. Non-diverging solutions (Kundt's class)
    32. Kerr–Schild metrics
    33. Algebraically special perfect fluid solutions
    Part IV. Special Methods:
    34. Applications of generation techniques to general relativity
    35. Special vector and tensor fields
    36. Solutions with special subspaces
    37. Local isometric embedding of four-dimensional Riemannian manifolds
    Part V. Tables:
    38. The interconnections between the main classification schemes
    References
    Index.

  • Authors

    Hans Stephani, Friedrich-Schiller-Universität, Jena, Germany
    Hans Stephani gained his diploma, Ph.D. and Habilitation at the Friedrich-Schiller-Universität Jena. He became Professor of Theoretical Physics in 1992, before retiring in 2000. He has been lecturing in theoretical physics since 1964 and has published numerous papers and articles on relativity and optics. He is also the author of four books.

    Dietrich Kramer, Friedrich-Schiller-Universität, Jena, Germany
    Dietrich Kramer is Professor of Theoretical Physics at the Friedrich-Schiller-Universität Jena. He graduated from this university, where he also finished his Ph.D. (1966) and Habilitation (1970). His current research concerns classical relativity. The majority of his publications are devoted to exact solutions in general relativity.

    Malcolm MacCallum, Queen Mary University of London
    Malcolm MacCallum is Professor of Applied Mathematics at the School of Mathematical Sciences, Queen Mary, University of London, where he is also Vice-Principal for Science and Engineering. He graduated from King's College, Cambridge and went on to complete his M.A. and Ph.D. there. His research covers general relativity and computer algebra, especially tensor manipulators and differential equations. He has published over 100 pages, review articles and books.

    Cornelius Hoenselaers, Loughborough University
    Cornelius Hoenselaers gained his Diploma at Technische Universität Karlsruhe, his D.Sc. at Hiroshima Daigaku and his Habilitation at Ludwig-Maximilian Universität München. He is Reader in Relativity Theory at Loughborough University. He has specialized in exact solutions in general relativity and other non-linear partial differential equations, and published a large number of papers, review articles and books.

    Eduard Herlt, Friedrich-Schiller-Universität, Jena, Germany
    Eduard Herlt is wissenschaftlicher Mitarbeiter at the Theoretisch Physikalisches Institut der Friedrich-Schiller-Universität Jena. Having studied physics as an undergraduate at Jena, he went on to complete his Ph.D. there as well as his Habilitation. He has had numerous publications including one previous book.

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