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

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.

Quantum properties of the Dirac field on BTZ black hole backgrounds

“…The latter strategy has been adopted also in [29]. To our best knowledge, a complete analysis of the Dirac equation, its separability, and the introduction of the Dirac Hamiltonian, with a complete determination of its spectral properties in the case of an uncharged rotating BTZ black hole solution is still lacking, and it is provided in the sequel.…”

2+1dimensional magnetically charged solutions in Einstein-power-Maxwell theory

“…It is interesting to note that, in contrast to the considered spacetime, the probe of naked singularity with Dirac fields in other 3D metrics, namely, BTZ [20] and matter coupled BTZ [23] spacetimes was shown to be quantum mechanically regular. It is also shown in this study that for general modes of spin zero Klein-Gordon fields, the spacetime is still singular.…”

“…The criterion of HM has been used in different spacetimes to investigate such classically naked singular spacetimes, i.e. whether they remain singular or not within the context of quantum mechanics [18][19][20][21][22][23][24].…”

A new Einstein-nonlinear electrodynamics solution in $$2+1$$ 2 + 1 dimensions

“…The main motivation to study the singularity is to clarify whether the uniform electric field in the angular direction has an effect on the resolution of this singularity or not. In order to compare the present study with the results obtained in [41], the singularity will be probed with two different quantum waves having spin structures 0 and 1/2, namely, bosonic waves and fermionic waves, respectively. The result of this investigation is that, with respect to the bosonic wave probe, the singularity remains quantum singular, whereas with respect to the fermionic wave probe the singularity is shown to be healed.…”

“…For specific values of the parameters, the timelike character of the naked singularity at r = 0 is also encountered in [40], in which a radial electric field is assumed within the context of NED with a power parameter k = 3/4. This singularity is investigated within the framework of quantum mechanics in [41]. Therein a timelike naked singularity is probed with quantum fields obeying the Klein-Gordon and Dirac equations.…”