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

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

2010-05-10

arxiv.org/abs/1005.1561v1

Eur.Phys.J.C71:1624,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages

Scientific paper

10.1140/epjc/s10052-011-1624-3

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.

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