Cosmological production of charged black hole pairs

We investigate the pair creation of charged black holes in a background with a positive cosmological constant. We consider $C$ metrics with a cosmological constant, and show that the conical singularities in the metric only disappear when it reduces to the Reissner-Nordstr\"om de Sitter metric. We construct an instanton describing the pair production of extreme black holes and an instanton describing the pair production of non-extreme black holes from the Reissner-Nordstr\"om de Sitter metric, and calculate their actions. There are a number of striking similarities between these instantons and the Ernst instantons, which describe pair production in a background electromagnetic field. We also observe that the type I instanton in the ordinary $C$ metric with zero cosmological constant is actually the Reissner-Nordstr\"om solution.