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  3. The Large Scale Structure of Space-Time
  • Cited by 5828
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2010
      May 1973
      ISBN:
      9780511524646
      9780521099066
      DOI:
      https://doi.org/10.1017/CBO9780511524646
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.54kg, 404 Pages
      • Subjects:
      Physics and Astronomy, Cosmology, Relativity and Gravitation, Theoretical Physics and Mathematical Physics
      Series:
      Cambridge Monographs on Mathematical Physics
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    • Selected: Digital
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    Subjects:
    Physics and Astronomy, Cosmology, Relativity and Gravitation, Theoretical Physics and Mathematical Physics
    Series:
    Cambridge Monographs on Mathematical Physics
    Information

    Book description

    Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

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    Contents

    Contents
    • Frontmatter
      pp i-vi
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    • Contents
      pp vii-x
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    • Preface
      pp xi-xii
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    • 1 - The role of gravity
      pp 1-9
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    • 2 - Differential geometry
      pp 10-55
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    • 3 - General Relativity
      pp 56-77
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    • 4 - The physical significance of curvature
      pp 78-116
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    • 5 - Exact solutions
      pp 117-179
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    • 6 - Causal structure
      pp 180-225
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    • 7 - The Cauchy problem in General Relativity
      pp 226-255
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    • 8 - Space–time singularities
      pp 256-298
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    • 9 - Gravitational collapse and black holes
      pp 299-347
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    • 10 - The initial singularity in the universe
      pp 348-364
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    • Appendix A - Translation of an essay by P. S. Laplace
      pp 365-368
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    • Appendix B - Spherically symmetric solutions and Birkhoff's theorem
      pp 369-372
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    • References
      pp 373-380
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    • Notation
      pp 381-384
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    • Index
      pp 385-391
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