The repulsive nature of naked singularities from the point of view of Quantum Mechanics

TL;DR

This paper investigates the quantum behavior near a naked Reissner-Nordström singularity using the Dirac equation, revealing that quantum effects render the singularity effectively repulsive and non-penetrable.

Contribution

It demonstrates that quantum mechanics regularizes the wave function at the singularity and shows the singularity's repulsive nature through probability density and current analysis.

Findings

Wave function remains regular at the singularity.

Probability density is zero at the singularity.

Radial current integral near the singularity is zero.

Abstract

We use the Dirac equation coupled to a background metric to examine what happens to quantum mechanical observables like the probability density and the radial current in the vicinity of a naked singularity of the Reissner-Nordstr\"{o}m type. We find that the wave function of the Dirac particle is regular in the point of the singularity. We show that the probability density is exactly zero at the singularity reflecting quantum-mechanically the repulsive nature of the naked singularity. Furthermore, the surface integral of the radial current over a sphere in the vicinity of the naked singularity turns out to be also zero.