Quantum (dis)charge of black hole interiors

TL;DR

This paper investigates quantum effects near the inner horizon of charged black holes, revealing that quantum polarization can either charge or discharge the horizon, with a tendency to discharge near extremality, and that quantum effects dominate classical ones.

Contribution

It provides a detailed analysis of quantum polarization effects at the inner horizon, showing their state-independent strength and impact on black hole interior dynamics.

Findings

Inner horizon can be charged or discharged depending on parameters.

Quantum effects dominate classical polarization effects.

Discharge occurs near extremality, affecting black hole evolution.

Abstract

We analyze the "vacuum" polarization induced by a quantum charged scalar field near the inner horizon of a charged (Reissner-Nordstr\"om-de Sitter) black hole in quantum states that start out as regular states near an initial Cauchy surface. Contrary to the outer (i.e. event-) horizon, where polarization effects lead to a discharge, we find that near an inner horizon, the transversal component of the expected current density can have either sign depending on the black hole and field parameters. Thus, the inner horizon can be charged or discharged. But we find that it is always discharged close to extremality thus driving the black hole interior away from this critical point. Furthermore, we find that quantum effects dominate in that the strength of the blow up of the quantum current at the inner horizon is state-independent and stronger than that of the current of a classical solution.