Magnetic Black Hole Pair-Production: One-Loop Tunneling Rate in the Weak Field Limit

TL;DR

This paper calculates the one-loop tunneling rate for magnetic black hole pair-production in weak magnetic fields, revealing quantum corrections that slightly modify the classical rate and persist even at extremality.

Contribution

It provides a detailed analysis of quantum fluctuations in the instanton geometry, extending previous work by including one-loop corrections in the pair-production rate.

Findings

One-loop corrections slightly reduce the tunneling exponent.

Quantum effects cause a semiclassical shift in black hole mass-to-charge ratio.

The correction persists even in the extremal black hole limit.

Abstract

Pair-production of magnetic Reissner-Nordstr\"{o}m black holes (of charges $\pm q$) is studied in the next-to-leading WKB approximation. We consider generic quantum fluctuations in the corresponding instanton geometry, a detailed study of which suggests that, for sufficiently weak field $B$, the problem can be reduced to that of quantum fluctuations around a single truncated near-extremal Euclidean black hole in thermal equilibrium. Typical one-loop contributions are such that the leading WKB exponent is corrected by a small fraction $\sim \hbar /q^2$. We show that this effect is merely due to a semiclassical shift of the black hole mass-to-charge ratio that persists even in the extremal limit. We close with a few final comments.