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

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}.