Action, entropy and pair creation rate of charged black holes in de Sitter space

TL;DR

This paper clarifies the Euclidean action for charged black holes in de Sitter space, relates it to horizon entropy, and estimates their pair creation rates, providing insights into black hole decay processes.

Contribution

It unifies the interpretation of Euclidean actions for various black holes in de Sitter space and applies this to estimate pair creation probabilities and decay mechanisms.

Findings

On-shell Euclidean action equals negative sum of horizon entropies.

Derived pair creation rates for black holes with arbitrary charge and mass.

Suggested decay pathways for extremal charged Nariai black holes.

Abstract

We compute and clarify the interpretation of the on-shell Euclidean action for Reissner-Nordstr\"{o}m black holes in de Sitter space. We show the on-shell action is minus the sum of the black hole and cosmological horizon entropy for arbitrary mass and charge in any number of dimensions. This unifying expression helps to clear up a confusion about the Euclidean actions of extremal and ultracold black holes in de Sitter, as they can be understood as special cases of the general expression. We then use this result to estimate the probability for the pair creation of black holes with arbitrary mass and charge in an empty de Sitter background, by employing the formalism of constrained instantons. Finally, we suggest that the decay of charged de Sitter black holes is governed by the gradient flow of the entropy function and that, as a consequence, the regime of light, superradiant, rapid charge emission should describe the potential decay of extreme charged Nariai black holes to singular geometries.