Uniqueness of extremal charged black holes in de Sitter

Abstract

We prove a uniqueness theorem for the charged Nariai black holes and ultracold black holes in four dimensions. In particular, we show that an analytic solution to four-dimensional Einstein-Maxwell theory with a positive cosmological constant containing a static extremal Killing horizon with spherical cross-sections of large radius (compared to the cosmological scale), must be locally isometric to the extremal Reissner-Nordström-de Sitter black hole or its near-horizon geometry. The theorem generalises to extremal static horizons with small radius, establishing uniqueness of cold black holes for generic values of the radius.

18 pages, 2 figures

References in corpus (9)

• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Symmetries of Higher Dimensional Black Holes
• Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes
• On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions
• Almost all extremal black holes in AdS are singular
• Einstein--Weyl Spaces and Near-Horizon Geometry
• Uniqueness of supersymmetric AdS${}_5$ black holes with $SU(2)$ symmetry
• On the uniqueness of supersymmetric AdS${}_5$ black holes with toric symmetry
• Uniqueness of the extremal Schwarzschild de Sitter spacetime

Cited by in corpus (1)

• Transverse expansion of the metric at null hypersurfaces I. Uniqueness and application to Killing horizons