Affine Quantization of the Interior Schwarzschild Black Hole
Morteza Bajand, Babak Vakili
TL;DR
The paper treats the Schwarzschild black hole interior as a time-dependent, spherically symmetric minisuperspace with two dynamical variables and applies affine quantization to handle the positive-definite configuration variable. This yields a Wheeler-DeWitt equation in the affine framework, allowing for analytically tractable eigenfunctions and a coherent wave packet that represents the quantum interior. The resulting quantum state shows a strong tendency to avoid the classical singularity, demonstrated by a negligible relative probability near the singular locus and a finite, large expectation value for the interior lapse-related parameter $\\nu$.Together, these findings provide concrete evidence that affine quantization can produce a nonsingular interior geometry for black holes and motivate its use in quantum gravity studies.
Abstract
In this paper, we investigate the Hamiltonian formulation of a spherically symmetric spacetime that corresponds to the interior of a Schwarzschild black hole. The resulting phase space involves two independent dynamical variables along with their conjugate momenta. We quantize the associated minisuperspace using the affine quantization method, which is particularly suited for systems with positive-definite configuration variables. We then explore whether the quantum effects encoded in this wave function can lead to the avoidance of classical singularities.