Schwinger Effect of Extremal Reissner-Nordstr\"om Black Holes

TL;DR

This paper analyzes the spatial profile of the Schwinger effect in extremal Reissner-Nordström black holes, revealing it peaks at the horizon and diminishes outward, consistent with the Weak Gravity Conjecture.

Contribution

It provides a full spatial analysis of the Schwinger effect in the entire black hole geometry, extending previous horizon-only results.

Findings

Schwinger effect strongest at the horizon

Decays with distance from the horizon

Switches off near the extremality bound

Abstract

The Schwinger effect has a variety of physics applications. In the context of black hole physics, it provides a channel for the decay of charged black holes. While the Schwinger rate has been derived for extremal Reissner-Nordstr\"om (RN) black hole using the $AdS_2\times S^2$ geometry of the horizon, a full analysis in the whole geometry is lacking, begging the question of whether it is sufficient to ignore contributions away from the horizon. In this paper, we address this problem and obtain the spatial profile of the Schwinger production rate in an asymptotically flat RN black hole spacetime. We find that the Schwinger effect is strongest on the horizon and decays with distance from the horizon, exhibiting a characteristic scale of the Compton wavelength of the particle. The rate is switched off when the particle's charge-to-mass ratio approaches the corresponding extremality bound for black holes, in accordance with a strong form of the Weak Gravity Conjecture (WGC).