Action, entropy and pair creation rate of charged black holes in de Sitter space
arxiv(2022)
摘要
We compute and clarify the interpretation of the on-shell Euclidean action
for Reissner-Nordström 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.
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