Non-Existence of Time-Periodic Solutions of the Dirac Equation in a Reissner-Nordstrom Black Hole Background

TL;DR

This paper proves analytically that the Dirac equation admits no normalizable, time-periodic solutions in a Reissner-Nordstrom black hole background, implying particles cannot remain in stable, periodic orbits around such black holes.

Contribution

It provides a rigorous proof that no time-periodic solutions exist for the Dirac equation in this black hole spacetime, clarifying particle behavior near charged black holes.

Findings

No normalizable, time-periodic Dirac solutions in Reissner-Nordstrom background

Particles either fall into the black hole or escape to infinity

Static solutions of the Dirac equation do not exist in this setting

Abstract

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordstrom black hole background; in particular, there are no static solutions of the Dirac equation in such a background field. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.