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.Comment: RevTeX4, 7 pages, 4 figures: new section about HWF added for clarity,
references updated, results unchanged. Version to appear in JHE
