Square-root quantization: application to quantum black holes

TL;DR

This paper compares two quantization methods for relativistic radial motion, revealing a sqrt{n} mass spectrum for quantum black holes, with implications for understanding their quantum properties.

Contribution

It introduces a novel application of quantization techniques to quantum black holes, deriving a specific mass spectrum that differs from traditional models.

Findings

Lorentzian time yields a Sommerfeld spectrum.

Quantum black holes exhibit a sqrt{n} mass spectrum.

Results are slightly dependent on the choice of time.

Abstract

Two different ways of quantizing the relativistic Hamiltonian for radial motion in the field of Coulomb-like potential are compared. The results depend slightly on choice of time. In the case of Lorentzian time a Sommerfeld spectrum is recovered. Application to quantum black holes gives a sqrt{n} mass spectrum with about the same numerical factors.