Quantum geometrodynamics for black holes and wormholes

TL;DR

This paper develops a quantum geometrodynamics framework for black holes and wormholes, deriving a finite difference Schroedinger equation and analyzing the discrete spectra of bound states in the large black hole limit.

Contribution

It introduces a novel quantum geometrodynamics approach with a finite difference Schroedinger equation for spherical gravity with a dust shell source.

Findings

Discrete spectra for quantum black holes and wormholes are obtained.

Spectra depend on two quantum numbers and are approximately quasicontinuous.

Large black hole approximation simplifies the spectral analysis.

Abstract

The geometrodynamics of the spherical gravity with a selfgravitating thin dust shell as a source is constructed. The shell Hamiltonian constraint is derived and the corresponding Schroedinger equation is obtained. This equation appeared to be a finite differences equation. Its solutions are required to be analytic functions on the relevant Riemannian surface. The method of finding discrete spectra is suggested based on the analytic properties of the solutions. The large black hole approximation is considered and the discrete spectra for bound states of quantum black holes and wormholes are found. They depend on two quantum numbers and are, in fact, quasicontinuous.