Uniqueness of Extremal Kerr and Kerr-Newman Black Holes

Abstract

We prove that the only four dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a longstanding gap in the black hole uniqueness theorems.

12 pages, v2: important references to earlier work added, v3: minor clarifications

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• Vanishing Love of Black Holes in General Relativity: From Spacetime Conformal Symmetry of a Two-dimensional Reduced Geometry
• Constructive proof of the Kerr-Newman black hole uniqueness including the extreme case
• Transverse deformations of extreme horizons
• Conformal mechanics inspired by extremal black holes in d=4
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• A Uniqueness theorem for black holes with Kaluza-Klein asymptotic in 5D Einstein-Maxwell gravity
• Some spacetimes containing non-rotating extremal isolated horizons
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• Conformal Symmetries of the Einstein-Hilbert Action on Horizons of Stationary and Axisymmetric Black Holes
• Uniqueness of extremal isolated horizons and their identification with horizons of all type D black holes
• Extremal horizons stationary to the second order: new constraints
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• Uniqueness of extremal charged black holes in de Sitter
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