Taming the classically divergent curvature in self-adjoint quantum black holes

Abstract

It is well-known that the Kretschmann curvature diverges strongly at the classical singularity of the black hole interior. In this paper, we are therefore interested in whether such a strong divergence can be tamed quantum mechanically in the vicinity of the black hole singularity. For this purpose, we consider DeWitt-regular quantum black hole solutions of a self-adjoint Wheeler–DeWitt equation originating from a Kantowski-Sachs representation of the black hole interior, coupled with a Klein–Gordon field that accounts for the existence of zero-point quantum vacuum fluctuations. We find that there exist regular quantum black holes with self-adjoint Hamiltonians having well-behaved Kretschmann curvature in the vicinity of the singularity, tamed by stronger restrictions on the eigenvalues than ones required by the DeWitt boundary condition. Consequently, the Kretschmann-regular black holes are found in smaller but still infinite domains in the space of eigenvalues allowed by the DeWitt criterion. Furthermore, we find that other relevant classically diverging quantities pose no threat as their quantum mechanical counterparts are well-behaved in the vicinity of the singularity.