Near-extremal limits of de Sitter black holes

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 AdS₂ x S², dS₂ x S², Mink₂ x S², 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 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 response in comparison to the other two near-extremal limits.