Uniqueness of extreme horizons in Einstein-Yang-Mills theory

Abstract

We consider stationary extreme black hole solutions to the Einstein-Yang-Mills equations in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS(2) symmetry and deduce its near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman (AdS) black hole. We also show that the near-horizon geometry of any static black hole is a direct product of AdS(2) and a constant curvature space.

12 pages

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Cited by in corpus (6)

• Classification of near-horizon geometries of extremal black holes
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• The Petrov type D equation on genus $>0$ sections of isolated horizons
• Extremal isolated horizons with $\Lambda$ and the related unique type D black holes
• Uniqueness of extremal isolated horizons and their identification with horizons of all type D black holes
• A2: Mathematical relativity and other progress in classical gravity theory - a session report