Black Hole Uniqueness Theorems

Markus Heusler

doi:10.1017/CBO9780511661396

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. Strong emphasis is given to the geometrical concepts. The general features of stationary black holes and the laws of black hole mechanics are then reviewed. Critical steps towards the proof of the 'no-hair' theorem are then discussed, including the methods used by Israel, the divergence formulae derived by Carter, Robinson and others, and finally the sigma model identities and the positive mass theorem. The book is rounded off with an extension of the electro-vacuum uniqueness theorem to self-gravitating scalar fields and harmonic mappings. This volume provides a rigorous textbook for graduate students in physics and mathematics. It also offers an invaluable, up-to-date reference for researchers in mathematical physics, general relativity and astrophysics.

‘This work in the Cambridge Lecture Notes in Physics series should be useful to everyone interested in stationary black hole systems. It contains copious references and provides easy access to a large amount of information about these systems as well as details of the uniqueness theorems themselves … a welcome addition to the literature on black holes.’

D. C. Robinson Source: Classical Quantum Gravity

‘Students and researchers into Michell holes will find this text (in lecture form) invaluable.’

A. D. Andrews Source: Irish Astronomical Journal

‘Black Hole Uniqueness Theorems, is a valuable addition to the literature on the mathematical theory of stationary black holes … The author has succeeded in presenting a self-contained account of black hole uniqueness theorems … I can recommend this book strongly to readers interested in black holes.’

Pawel O. Mazur Source: General Relativity and Gravitation

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Black Hole Uniqueness Theorems

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xiv

1 - Preliminaries
pp 1-5

2 - Spacetimes admitting Killing fields
pp 6-30

3 - Circular spacetimes
pp 31-41

4 - The Kerr metric
pp 42-55

5 - Electrovac spacetimes with Killing fields
pp 56-83

6 - Stationary black holes
pp 84-101

7 - The four laws of black hole physics
pp 102-121

8 - Integrability and divergence identities
pp 122-139

9 - Uniqueness theorems for nonrotating holes
pp 140-165

10 - Uniqueness theorems for rotating holes
pp 166-179

11 - Scalar mappings
pp 180-204

12 - Self–gravitating harmonic mappings
pp 205-229

References
pp 230-245

Index
pp 246-249

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