On Pair Creation of Extremal Black Holes and Kaluza-Klein Monopoles

TL;DR

This paper investigates the classical and quantum aspects of extremal black holes and Kaluza-Klein monopoles, showing their pair creation via instantons in a magnetic field and connecting their actions to known physical results.

Contribution

It provides a detailed analysis of extremal black hole solutions, their reduction to static forms, and the interpretation of their Euclidean sections as instantons for pair creation, including quantum corrections.

Findings

Extremal solutions reduce to static black holes near the horizon.

Euclidean sections serve as instantons for pair creation in magnetic fields.

Instanton actions match Schwinger results in weak fields.

Abstract

Classical solutions describing charged dilaton black holes accelerating in a background magnetic field have recently been found. They include the Ernst metric of the Einstein-Maxwell 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.