Quantized Black Hole and Heun function

TL;DR

This paper explores the quantization of black holes using a Bohr-inspired approach, linking the eigenvalue problem to the Heun differential equation, and discusses the solvability of the associated wave equation.

Contribution

It introduces a method to determine black hole spectra through the Heun differential equation, extending previous models with a new mathematical framework.

Findings

Eigenfunctions reduce to HeunB differential equation

Black hole spectrum can be obtained from solving Heun's equation

Superficial solution of the Schrödinger equation presented

Abstract

Following the simple proposal by He and Ma for quantization of a black hole(BH) by Bohr's idea about the atoms, we discussed the solvability of the wave equation for such a BH. We superficial solved the associated Schrodinger equation. The eigenfunction problem reduces to HeunB $H$ differential equation which is a natural generalization of the hypergeometric differential equation. In other words, the spectrum can be determined by solving the Heun's differential equation.