Pair Creation of Dilaton Black Holes

TL;DR

This paper constructs new exact solutions in dilaton gravity theories, generalizing known metrics to include accelerating dilaton black holes and instantons for pair creation, with specific topologies and parameter restrictions.

Contribution

It introduces a solution generating technique for dilaton C-metrics and extends instanton constructions to various dilaton coupling regimes.

Findings

Generalized C-metrics for dilaton black holes with acceleration

Embedded these solutions in magnetic dilaton Melvin backgrounds

Constructed instantons describing pair creation with specific topologies

Abstract

We consider dilaton gravity theories in four spacetime dimensions parametrised by a constant $a$, which controls the dilaton coupling, and construct new exact solutions. We first generalise the C-metric of Einstein-Maxwell theory ($a=0$) to solutions corresponding to oppositely charged dilaton black holes undergoing uniform acceleration for general $a$. We next develop a solution generating technique which allows us to ``embed" the dilaton C-metrics in magnetic dilaton Melvin backgrounds, thus generalising the Ernst metric of Einstein-Maxwell theory. By adjusting the parameters appropriately, it is possible to eliminate the nodal singularities of the dilaton C-metrics. For $a<1$ (but not for $a\ge 1$), it is possible to further restrict the parameters so that the dilaton Ernst solutions have a smooth euclidean section with topology $S^2\times S^2-{\rm\{pt\}}$, corresponding to instantons describing the pair production of dilaton black holes in a magnetic field. A different restriction on the parameters leads to smooth instantons for all values of $a$ with topology $S^2\times \R^2$.