Entropy in black hole pair production

Abstract

Pair production of Reissner-Nordstr\"om black holes in a magnetic field can be described by a Euclidean instanton. It is shown that the instanton amplitude contains an explicit factor of ${e}^{\frac{A}{4}}$, where $A$ is the area of the event horizon. This is consistent with the hypothesis that ${e}^{\frac{A}{4}}$ measures the number of black hole states.