Cosmological production of charged black hole pairs

TL;DR

This paper studies the quantum pair creation of charged black holes in a universe with a positive cosmological constant, using instanton methods and analyzing the related metrics.

Contribution

It constructs instantons for pair production of both extreme and non-extreme charged black holes in de Sitter space, revealing new insights into their geometric and physical properties.

Findings

Instantons for black hole pair creation are constructed and their actions calculated.

Discovered similarities between these instantons and Ernst instantons in electromagnetic backgrounds.

Revealed that the zero cosmological constant case reduces to the Reissner-Nordström solution.

Abstract

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.