Global Aspects in Gravitation and Cosmology

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This book describes several basic results and applications of global aspects in gravitation theory and cosmology within the framework of Einstein's theory of gravity. Topics include results on the structure and topology of space-time, exact solutions to Einstein equations and singularities, the status of quantum gravity, and quantum effects near space-time singularities in strong curvature fields. Also covered are the global upper limits in cosmology on elementary particle masses which might constitute the dark matter of the universe. After discussing in detail the fundamental role played by global considerations in gravity and general relativity, the author points out the significant problems that remain: the nature and structure of space-time singularities, the cosmic censorship problem in black hole physics, and the issue of quantum effects in strong gravity fields. The author's treatment of gravitational collapse illustrates how powerfully-strong curvature naked singularities could result from the continual gravitational collapse of matter with several reasonable equations of state--including inflowing radiation, dust, or a perfect fluid. Students and mathematicians, astrophysicists, and physicists will find this theoretically rich book a landmark in relativity theory.
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Product Details

Table of Contents

1 Global themes in gravity 1
2 The manifold model for space-time 12
3 Solutions to the Einstein equations 56
4 Causality and space-time topology 98
5 Singularities in general relativity 157
6 Gravitational collapse and cosmic censorship 181
7 General constraints on naked singularity formation 256
8 Global upper limits in cosmology 286
9 Quantum effects near the space-time singularity 313
References 357
Index 371
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