Canonical Quantization of Neutral and Charged Static Black Hole as a Gravitational Atom

TL;DR

This paper develops a canonical quantization approach for particles around black holes, revealing a gravitational atom analogy with quantized energy levels and graviton emissions that encode black hole properties.

Contribution

It introduces a novel quantization method for particles in black hole gravitational fields, deriving exact energy levels and wave functions, and linking transitions to graviton emissions.

Findings

Exact quantized energy levels for particles near black holes

Wave functions form quasibound states due to strong gravity and horizons

Particle transitions emit gravitons carrying black hole information

Abstract

The gravitational field is usually neglected in the calculation of atomic energy levels as its effect is much weaker than the electromagnetic field, but that is not the case for a particle orbiting a black hole. In this work, the canonical quantization of a massive and massless particles under gravitational field exerted by this tiny but very massive object, both neutral and charged, is carried out. By using this method, a very rare exact result of the particle's quantized energy can be discovered. The presence of a very strong attractive field and also the horizon make the energy complex valued and force the corresponding wave function to be a quasibound state. Moreover, by taking the small scale limit, the system becomes a gravitational atom in the sense of Hydrogenic atoms energy levels and its wave function can be rediscovered. Moreover, analogous to electronic transitions, the transition of the particle in this case emits a graviton which carries a unique fingerprint of the black hole such as black hole's mass and charge.