Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

TL;DR

This paper investigates quantum singularities in (2+1)-dimensional charged and dilaton black hole spacetimes, showing that quantum effects can remove classical singularities for fermions but not for scalar particles.

Contribution

It extends the analysis of quantum singularities to charged BTZ and Einstein-Maxwell-dilaton spacetimes, revealing matter-dependent quantum regularity of classical singularities.

Findings

Quantum test fields remove conical geometry near r=0.

Klein-Gordon particles see the singularity as quantum mechanically singular.

Dirac fermions perceive the singularity as nonsingular.

Abstract

Quantum singularities considered in the 3D BTZ spacetime by Pitelli and Letelier (Phys. Rev. D77: 124030, 2008) is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and non-linear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analysed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields; the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying Klein-Gordon equation but nonsingular for fermions obeying Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes do not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.