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The Large Scale Structure of Space-Time
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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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‘The book is a masterpiece, written by sure hands.’

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Contents

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

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