Black Hole Uniqueness Theorems

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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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Editorial Reviews

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"...this volume is in fact well-written and provides a quite rigorous and advanced textbook for graduate students in mathematical physics as well as an important reference for researchers who are interested in the 'classical' theory of black holes and, in particular, in uniqueness offers an up-to-date bibliography also taking account of several links with problems currently under investigation which are given throughout the book." Valter Moretti, Mathematical Reviews
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Product Details

  • ISBN-13: 9780521567350
  • Publisher: Cambridge University Press
  • Publication date: 2/28/2003
  • Series: Cambridge Lecture Notes in Physics Series, #6
  • Pages: 263
  • Product dimensions: 6.00 (w) x 8.90 (h) x 0.80 (d)

Table of Contents

1. Preliminaries; 2. Spacetimes admitting killing fields; 3. Circular spacetimes; 4. The Kerr metric; 5. Electrovac spacetimes with killing fields; 6. Stationary black holes; 7. The laws of black hole physics; 8. Integrability and divergence identities; 9. Uniqueness theorems for nonrotating holes; 10. Uniqueness theorems for rotating holes; 11. Scalar mappings; 12. Self-gravitating harmonic mappings; References; Subject index.

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