Regularity of quantum geometry at the black hole singularity

In this paper, we examine quantum mechanical operators whose classical counterparts, that define the interior geometry, diverge at the black hole singularity. We, therefore, analyze the integrals determining the expectation values of those operators with respect to wave functions coming from regular solutions of the Wheeler–DeWitt equation in a minisuperspace model of the black hole. We find that there exist inequalities among the eigenvalues, leading to the existence of black holes regular in all respects, in the sense that the quantum operators as well as the wave function are well behaved and finite in the vicinity of the singularity. This implies complete regularity of the quantum spacetime at the black hole singularity.