Charged Topological Black Hole Pair Creation

TL;DR

This paper investigates the pair creation of charged and neutral topological black holes in spacetimes with a cosmological constant, analyzing instantons and Euclidean actions for various horizon topologies and conditions.

Contribution

It classifies black hole solutions with different horizon topologies where conical singularities vanish and explores pair creation processes including negative mass black holes.

Findings

Black hole pair creation occurs for various topologies with domain walls.

Explicit instantons and Euclidean actions are derived for each case.

Non-static solutions only exist for spherical topologies.

Abstract

I examine the pair creation of black holes in spacetimes with a cosmological constant of either sign. I consider cosmological C-metrics and show that the conical singularities in this metric vanish only for three distinct classes of black hole metric, two of which have compact event horizons on each spatial slice. One class is a generalization of the Reissner-Nordstrom (anti) de Sitter black holes in which the event horizons are the direct product of a null line with a 2-surface with topology of genus $g$. The other class consists of neutral black holes whose event horizons are the direct product of a null conoid with a circle. In the presence of a domain wall, black hole pairs of all possible types will be pair created for a wide range of mass and charge, including even negative mass black holes. I determine the relevant instantons and Euclidean actions for each case. Only for spherical are non-static solutions possible.