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

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 comment that the decay of charged de Sitter black holes is expected to be governed by the gradient flow of the entropy function, and that as a consequence, as long as the regime of light, superradiant, rapid charge emission is excluded, the effective decay may be described by the tunneling formalism.Comment: 27 pages, 9 figure