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.

arXiv comment18 pages, 2 figures

References in corpus (27)

• Stationary Black Holes: Uniqueness and Beyond
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Classification of near-horizon geometries of extremal black holes
• Symmetries of Higher Dimensional Black Holes
• Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions
• Towards the classification of static vacuum spacetimes with negative cosmological constant
• On non-existence of static vacuum black holes with degenerate components of the event horizon
• The structure of the extreme Schwarzschild-de Sitter space-time
• On Israel-Wilson-Perjes 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
• Uniqueness of Extremal Kerr and Kerr-Newman Black Holes
• The classification of static electro--vacuum space--times containing an asymptotically flat spacelike hypersurface with compact interior
• Almost all extremal black holes in AdS are singular
• On the uniqueness of extremal vacuum black holes
• Transverse deformations of extreme horizons
• Static Einstein-Maxwell black holes with no spatial isometries in AdS space
• A uniqueness theorem for degenerate Kerr-Newman black holes
• On the uniqueness of Schwarzschild-de Sitter spacetime
• Three-dimensional black holes and descendants
• Non-singular, vacuum, stationary space-times with a negative cosmological constant
• 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
• Electrovacuum spacetime near an extreme horizon
• Uniqueness of the extremal Schwarzschild de Sitter spacetime
• Moduli Spaces of Transverse Deformations of Near-Horizon Geometries

Cited by in corpus (1)

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