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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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