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 AdS2 symmetry and deduce that 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 AdS2 and a constant curvature space.Communicated by H Reall
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