Near-Extremal Limits of de Sitter Black Holes

Abstract

We analyze the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with near-horizon geometries AdS${}_2\times S^2$, dS${}_2\times S^2$, Mink${}_2\times S^2$, respectively. For each of these three cases we analyze small deformations away from extremality, and contrast their response. We also construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features and we provide a more detailed analysis of the perturbations around the near-horizon geometry for each case. Our results for the ultracold case in particular show an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

arXiv comment32 pages, 2 figures; v3: typos fixed, clarifications on branches of 2D solutions added, comments on metric backreaction in sec. 4.2 removed. Section with outlook and conclusions added

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• The fate of Reissner--Nordström--de Sitter black holes: nonequilibrium discharge and evaporation
• The Fate of Nucleated Black Holes in de Sitter Quantum Gravity