Inner Horizon of the Quantum Reissner-Nordstr\"om Black Holes

TL;DR

This paper investigates the quantum properties of Reissner-Nordström black holes, revealing that quantum effects can suppress the formation of the inner horizon at near-Planckian masses, challenging classical instability expectations.

Contribution

It introduces a quantum horizon wave-function approach to analyze the inner horizon, showing that quantum effects can eliminate the inner horizon under certain conditions.

Findings

Inner horizon probability is negligible near the Planck scale.

Quantum effects may prevent classical inner horizon instabilities.

Inner horizon formation depends on black hole mass and charge.

Abstract

We study the nature of the inner Cauchy horizon of a Reissner-Nordstr\"om black hole in a quantum context by means of the horizon wave-function obtained from modelling the electrically charged source as a Gaussian wave-function. Our main finding it that there is a significant range of black hole mass (around the Planck scale) and specific charge for which the probability of realizing the inner horizon is negligible. This result suggests that any semiclassical instability one expects near the inner horizon may not be occur in quantum black holes.