Energy quantization for matter orbiting black hole and Hawking radiation

TL;DR

This paper explores how energy quantization of particles orbiting black holes relates to Hawking radiation and the Unruh effect, suggesting potential observational signatures in hydrogen line emissions around primordial black holes.

Contribution

It introduces a quantization model for orbiting particles' energy near black holes and links it to Hawking radiation and the Unruh effect, proposing observable consequences.

Findings

Energy levels resemble Hawking temperature

Quantization consistent with Unruh effect

Potential observability via hydrogen line emissions

Abstract

The energy of a test particle orbiting a Schwarzschild black hole is quantized owing to the quantization of the angular momentum. For smallest stable circular orbit, the excitation energy is found to resemble closely the expression for the temperature of the Hawking radiation. This result is consistent with the Unruh effect for orbiting test particle. The predicted energy quantization might be observable by studies of the red-shifted 21-cm line of neutral hydrogen orbiting a primordial black hole with mass of the order of that of Earth.