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An Introduction to General Relativity

An Introduction to General Relativity

textbook

Part of London Mathematical Society Student Texts

  • Date Published: January 1991
  • availability: Available
  • format: Paperback
  • isbn: 9780521339438

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  • This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.

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    Product details

    • Date Published: January 1991
    • format: Paperback
    • isbn: 9780521339438
    • length: 192 pages
    • dimensions: 230 x 153 x 14 mm
    • weight: 0.29kg
    • contains: 32 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    1. Introduction
    2. Vectors and tensors in flat three-space
    3. Aspects of special relativistic geometry
    4. Tensor analysis on manifolds
    5. Covariant differentiation
    6. Properties of the Riemann tensor
    7. Riemannian geometry
    8. The Lie derivative
    9. Geodesics
    10. Geodesic deviation
    11. Differential forms
    12. The transition from Newtonian theory
    13. Einstein's field equations
    14. The slow motion approximation
    15. The Schwarzschild solution
    16. Gravitational red-shift and time dilation
    17. The geodesic equation for the Schwarzschild solution
    18. Classical tests
    19. The extended Schwarzschild solution
    20. Black holes and gravitational collapse
    21. Interior solutions
    22. The Kerr solution
    23. Homogeneous and isotropic three-spaces
    24. Cosmology: kinematics
    25. Cosmology: dynamics
    25. Anisotropic cosmologies
    Index.

  • Authors

    L. P. Hughston, King's College London

    K. P. Tod, University of Oxford

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