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Exact Solutions in Three-Dimensional Gravity


Part of Cambridge Monographs on Mathematical Physics

  • Author: Alberto A. García-Díaz, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV)
  • Date Published: September 2017
  • availability: Available
  • format: Hardback
  • isbn: 9781107147898

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About the Authors
  • A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravities, and therefore providing graduates and researchers with an invaluable resource on this important topic in gravitational physics. Including contributions by David Chow, Christopher N. Pope and Ergin Sezgin (chapters 16-19).

    • The first book in the field of 2+1 gravity to examine solutions of physical interest
    • All the physical and mathematical concepts required are explained in the text, enabling readers to gain a complete understanding of the complexities of the field
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    Reviews & endorsements

    '2+1 dimensions is the lowest dimension in which Einstein gravity works, and it exhibits some interesting features, such as space-time being flat where there is no matter. The topic has been studied for about 50 years, and there are, remarkably, large numbers of exact solutions that have been found. This book presents a comprehensive account of them … It is obviously a labour of love, which runs to over 400 pages, and which will be of interest to relativists, providing links between the solutions and those for the more familiar 3+1 space- time.' Alan Heavens, The Observatory

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    Product details

    • Date Published: September 2017
    • format: Hardback
    • isbn: 9781107147898
    • length: 450 pages
    • dimensions: 254 x 180 x 30 mm
    • weight: 0.97kg
    • contains: 37 tables
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Point particles
    3. Dust solutions
    4. AdS cyclic symmetric stationary solutions
    5. Perfect fluid static stars
    6. Static perfect fluid stars with Λ
    7. Hydrodynamic equilibrium
    8. Stationary perfect fluid with Λ
    9. Friedmann–Robertson–Walker cosmologies
    10. Dilaton-inflaton FRW cosmologies
    11. Einstein–Maxwell solutions
    12. Nonlinear electrodynamics black hole
    13. Dilaton minimally coupled to gravity
    14. Dilaton non-minimally coupled to gravity
    15. Low energy 2+1 string gravity
    16. Topologically massive gravity
    17. Bianchi type spacetimes in TMG
    18. Petrov type N wave metrics
    19. Kundt spacetimes in TMG
    20. Cotton tensor in Riemannian spacetimes

  • Author

    Alberto A. García-Díaz, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV)
    Alberto A. García-Díaz is Emeritus Professor at the Center for Research and Advanced Studies of the National Polytechnic Institute, Mexico (CINVESTAV-IPN). His research throughout his career has focused on algebraic classification in four dimensional gravity, nonlinear electrodynamics and dilaton fields.

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