Pair creation of dilaton black holes

We consider dilaton gravity theories in four spacetime dimensions parametrized by a constant a, which controls the dilaton coupling, and construct new exact solutions. We first generalize 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 generalizing 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≥1), it is possible to further restrict the parameters so that the dilaton Ernst solutions have a smooth Euclidean section with topology ${\mathit{S}}^2$×${\mathit{S}}^2$-{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 ${\mathit{S}}^2$×${\mathit{openR}}^2$.