Spinorial Wheeler-DeWitt wave functions inside black hole horizons

TL;DR

This paper explores spinorial solutions to the Wheeler-DeWitt equation inside black hole horizons, applying Yeom's interpretation and introducing Dirac-type equations to better understand quantum black hole interiors.

Contribution

It introduces a spinorial approach to the Wheeler-DeWitt equation inside black holes and applies Yeom's interpretation to these solutions, extending previous quantum cosmology methods.

Findings

Spinorial wave functions are consistent with Yeom's interpretation.

Solutions are similar for different black hole topologies.

Wave packet analysis supports the interpretation's validity.

Abstract

We revisit the solutions of the Wheeler-DeWitt (WDW) equation inside the horizons of spherical black holes and planar topological black holes in arbitrary dimensions. For these systems, the solutions of the equations are found to have the same form. Therefore, Yeom's Annihilation-to-nothing interpretation can be applied to each case. We have introduced the Dirac-type WDW equations into quantum cosmology in a recent paper, so we also apply our formulation to the quantum theory of the interior of the black hole in order to obtain the solution of the spinorial wave function. The shape of the wave packet of the spinorial WDW wave function indicates that the variation of Yeom's interpretation holds in this scheme.