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 ≥ 1), it is possible to further restrict the parameters so that the dilaton Ernst solutions have a smooth euclidean section with topology S 2 × S 2 − {pt}, corresponding to instantons * Address from 1st Oct. 1993: Relativity Group Department of Physics, University of California, Santa Barbara, CA 93106.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

Classical solutions describing charged dilaton black holes accelerating in a background magnetic field have recently been found. They include the Ernst metric of the EinsteinMaxwell theory as a special case. We study the extremal limit of these solutions in detail, both at the classical and quantum levels. It is shown that near the event horizon, the extremal solutions reduce precisely to the static extremal black hole solutions. For a particular value of the dilaton coupling, these extremal black holes are five dimensional Kaluza-Klein monopoles. The euclidean sections of these solutions can be interpreted as instantons describing the pair creation of extremal black holes/Kaluza-Klein monopoles in a magnetic field. The action of these instantons is calculated and found to agree with the Schwinger result in the weak field limit. For the euclidean Ernst solution, the action for the extremal solution differs from that of the previously discussed wormhole instanton by the Bekenstein-Hawking entropy. However, in many cases quantum corrections become large in the vicinity of the black hole, and the precise description of the creation process is unknown.