PAIR CREATION OF EXTREMAL BLACK-HOLES AND KALUZA-KLEIN MONOPOLES

Classical solutions describing charged dilaton black holes acceleratin g in a background magnetic field have recently been found. They includ e the Ernst metric of the Einstein-Maxwell theory as a special case. W e study the extremal limit of these solutions in detail, both at the c lassical and quantum levels. It is shown that near the event horizon t he extremal solutions reduce precisely to the static extremal black ho le solutions. For a particular value of the dilaton coupling, these ex tremal black holes are five-dimensional Kaluza-Klein monopoles. The Eu clidean sections of these solutions can be interpreted as instantons d escribing the pair creation of extremal black holes and/or Kaluza-Klei n monopoles in a magnetic field. The action of these instantons is cal culated 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 instan ton by the Bekenstein-Hawking entropy. However, in many cases quantum corrections become large in the vicinity of the black hole, and the pr ecise description of the creation process is unknown.