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Uniqueness of extremal black holes in de Sitter

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Uniqueness theorems for black holes with a cosmological constant are only known in a few limited cases. In my talk I present a recent uniqueness theorem for the extremal Schwarzschild-de Sitter black hole within the class of analytic vacuum spacetimes with a positive cosmological constant containing a static extremal Killing horizon. The proof is based on establishing the uniqueness of transverse deformations to the near-horizon geometry at each order in the transverse parameter. I also present a generalisation to charged extremal black holes in de Sitter and discuss the analogous problem in the case of negative cosmological constant. The talk is based on 2309.04238 [gr-qc] and 2403.08467 [gr-qc].

This talk is part of the DAMTP Friday GR Seminar series.

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