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By Markus Heusler
Publisher: Cambridge University Press
Print Publication Year:1996
Online Publication Date:March 2010
Online ISBN:9780511661396
Paperback ISBN:9780521567350
Book DOI: http://dx.doi.org/10.1017/CBO9780511661396
Subjects: Cosmology, Relativity and Gravitation , Cosmology, Relativity and Gravitation
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.
Reviews:
pp. i-vi
pp. vii-x
pp. xi-xiv
pp. 1-5
2 - Spacetimes admitting Killing fields: Read PDF
pp. 6-30
3 - Circular spacetimes: Read PDF
pp. 31-41
pp. 42-55
5 - Electrovac spacetimes with Killing fields: Read PDF
pp. 56-83
6 - Stationary black holes: Read PDF
pp. 84-101
7 - The four laws of black hole physics: Read PDF
pp. 102-121
8 - Integrability and divergence identities: Read PDF
pp. 122-139
9 - Uniqueness theorems for nonrotating holes: Read PDF
pp. 140-165
10 - Uniqueness theorems for rotating holes: Read PDF
pp. 166-179
11 - Scalar mappings: Read PDF
pp. 180-204
12 - Self–gravitating harmonic mappings: Read PDF
pp. 205-229
pp. 230-245
pp. 246-249