Rigidity of the extremal Kerr-Newman horizon

Abstract

We prove that the intrinsic geometry of compact cross-sections of an extremal horizon in four-dimensional Einstein-Maxwell theory must admit a Killing vector field or is static. This implies that any such horizon must be an extremal Kerr-Newman horizon and completes the classification of the associated near-horizon geometries. The same results hold with a cosmological constant.Comment: 7 page