The evaporation of near-extremal black holes through charged particle emission

TL;DR

This paper compares quantum and semi-classical emission rates of charged particles from near-extremal black holes, revealing size-dependent behaviors and unifying the understanding of black hole evaporation across different regimes.

Contribution

It introduces a unified framework for analyzing quantum and semi-classical emission rates of near-extremal black holes, highlighting size and energy regime differences using Schwarzian theory.

Findings

Quantum rate differs from semi-classical for small black holes at low energies.

Superradiant emission enhances quantum rates compared to semi-classical predictions.

For large black holes, quantum and semi-classical rates converge, recovering known suppression results.

Abstract

We compute the quantum rate for massless charged scalar emission by a near-extremal Reissner-Nordstr\"om black hole using Schwarzian theory as the effective description of the black hole. This is compared to the semi-classical Hawking rate which we also compute near extremality. We classify black holes into small and large, each with a unique spectrum. For small black holes, at energies below a particular quantum scale, the emission is captured by the quantum rate, which gives different predictions from the semi-classical. Furthermore, depending on how the energy compares to another scale associated with the phenomenon of superradiance, the radiation either comes out as mostly non-superradiant or mostly superradiant. For non-superradiant emission, it is found that the quantum rate is suppressed compared to the semi-classical in the same way as recently observed for neutral radiation. For superradiant emission, a novel behavior is observed, the quantum rate is enhanced compared to the semi-classical. For large black holes, we argue that the quantum rate always reduces to the semi-classical. In the limit of very large black holes, from our semi-classical rate, we recover the Gibbons result of Schwinger-like suppression. This gives a unified story of near-extremal charged emission rates, both quantum and semi-classical, which covers all sizes of black hole and all energy regimes. We use these rates to discuss the evaporation history of each type of black hole, from when it starts very near extremality, until it has left this regime. Finally, for the near-extremal Kerr black hole, we argue that the quantum rate always reduces to the semi-classical with the superradiant modes dominating. This rate is computed for spin $0,1,2$. Our analysis emphasizes the AdS$_2$ structure of the Reissner-Nordstr\"om and Kerr near-horizon regions, which enables a completely parallel treatment of the two.