Eur. Phys. J. C (2011) 71: 1624
https://doi.org/10.1140/epjc/s10052-011-1624-3

Regular Article - Theoretical Physics

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

¹ Department of Mathematics, University of West Indies, Kingston 6, Jamaica
² Departamento de Fisica, Universidad de los Andes, Cra. 1E No. 18A-10, Bogota, Colombia

^* e-mail: mnowakos@uniandes.edu.co

Received: 27 January 2011
Revised: 16 March 2011
Published online: 14 April 2011

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–Nordström 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.