Black Hole Uniqueness Theorems

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Cambridge University Press, Jul 25, 1996 - Science - 249 pages
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This timely review provides a self-contained introduction to the mathematical theory of stationary black holes and a self-consistent exposition of the corresponding uniqueness theorems. The opening chapters examine the general properties of space-times admitting Killing fields and derive the Kerr-Newman metric. Heusler emphasizes the general features of stationary black holes, the laws of black hole mechanics, and the geometrical concepts behind them. Tracing the steps toward the proof of the "no-hair" theorem, he illustrates the methods used by Israel, the divergence formulas derived by Carter, Robinson and others, and finally the sigma model identities and the positive mass theorem. The book also includes an extension of the electro-vacuum uniqueness theorem to self-gravitating scalar fields and harmonic mappings. A rigorous textbook for graduate students in physics and mathematics, this volume offers an invaluable, up-to-date reference for researchers in mathematical physics, general relativity and astrophysics.
 

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Contents

1 Preliminaries
1
2 Spacetimes admitting Killing fields
6
3 Circular spacetimes
31
4 The Kerr metric
42
5 Electrovac spacetimes with Killing fields
56
6 Stationary black holes
84
7 The four laws of black hole physics
102
8 Integrability and divergence identities
122
9 Uniqueness theorems for nonrotating holes
140
10 Uniqueness theorems for rotating holes
166
11 Scalar mappings
180
12 Selfgravitating harmonic mappings
205
References
230
Index
246
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