Pair production of black holes in a $U(1) \otimes U(1)$ theory

TL;DR

This paper explores exact solutions in a two-$U(1)$ gauge field theory with a dilaton, revealing instantons that describe the pair production of charged dilaton black holes, extending previous solutions with new topological features.

Contribution

It introduces new exact solutions analogous to classical C-metric and Ernst solutions, and constructs instantons for black hole pair production in a $U(1) imes U(1)$ theory.

Findings

Derived solutions with smooth Euclidean sections

Constructed instantons describing black hole pair production

Extended previous instanton solutions with new topologies

Abstract

Charged dilaton black hole solutions have recently been found for an action with two $U(1)$ gauge fields and a dilaton field. I investigate new exact solutions of this theory analogous to the C-metric and Ernst solutions of classical general relativity. The parameters in the latter solution may be restricted so that it has a smooth Euclidean section with topology $S^2 \times S^2 - \{pt\}$, which gives an instanton describing pair production of the charged dilaton black holes. These instantons generalise those found recently by Dowker {\it et al}.