Quantum Black Hole Model and Hawking's Radiation

TL;DR

This paper develops a quantum model of charged black holes using a finite difference Schrödinger equation, deriving a discrete mass spectrum compatible with Hawking radiation and suggesting a potential resolution to the information paradox.

Contribution

It introduces a novel quantum black hole model with a finite difference equation and analyzes its spectrum, connecting it to Hawking radiation and the information paradox.

Findings

Discrete, infinitely degenerate mass spectrum obtained

Quantum states compatible with Hawking radiation at low temperatures

Explicit ground state wave functions derived

Abstract

The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appeared to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking's radiation in the limit of low temperatures both for large and nearly extreme Reissner-Nordstrom black holes. The above mentioned infinite degeneracy of the mass (energy) eigenvalues may appeared helpful in resolving the well known information paradox in the black hole physics.