Inner Horizon of the Quantum Reissner-Nordström Black Holes

Abstract

We study the nature of the inner Cauchy horizon of a Reissner-Nordström 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.

arXiv commentRevTeX4, 7 pages, 4 figures: new section about HWF added for clarity, references updated, results unchanged. Version to appear in JHEP