Cosmic censorship and stationary states of half-spin particles in the field of Reissner-Nordstroem naked singularity

TL;DR

This paper investigates the quantum behavior of half-spin particles near Reissner-Nordstroem naked singularities, revealing potential barriers and the existence of bound states with specific energy conditions.

Contribution

It demonstrates that RN naked singularities are separated by infinite potential barriers for all Dirac particles and establishes conditions for bound state formation.

Findings

RN naked singularity is separated by an infinite potential barrier for all Dirac particles.

Bound states of half-spin particles can exist in the RN naked singularity field.

Energy eigenvalues and eigenfunctions for these bound states were computed.

Abstract

The paper explores quantum mechanics of half-spin particle motion in the field of Reissner-Nordstroem (RN) naked singularity. It is shown that for any quantum mechanical Dirac particle, irrespective of availability and sign of its electrical charge, the RN naked singularity is separated by an infinitely high positive potential barrier. With like charges of a particle and the source of the RN naked singularity, near the origin there exists the second completely impenetrable potential barrier. It has been proved that in the field of the RN naked singularity, bound states of half-spin particles can exist. The conditions for appearance of such states were revealed and computations were performed to find energy eigenvalues and eigenfunctions.