Near-Extremal Limits of de Sitter Black Holes

TL;DR

This paper investigates the thermodynamic behavior of charged de Sitter black holes near extremality, analyzing three distinct extremal limits and their near-horizon geometries, with a focus on effective theories and entropy-charge relationships.

Contribution

It introduces a detailed analysis of near-extremal limits of de Sitter black holes, including effective 2D theories and perturbation responses for each extremal case.

Findings

Distinct near-horizon geometries for each extremal limit.

Ultracold case shows unique entropy and charge variation interplay.

Effective 2D theories successfully capture near-horizon dynamics.

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.