Article

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

Physical review D: Particles and fields 04/2010; DOI: 10.1103/PhysRevD.82.084016
Source: arXiv

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. Comment: 13 pages, 1 figure. Final version, to appear in PRD

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ABSTRACT: A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied to a class of spherically symmetric, conformally static spacetimes, including as special cases those studied by Roberts, by Fonarev, and by Husain, Martinez, and N\'u\~nez. We use solutions of the generally coupled, massless Klein-Gordon equation as test fields. In this way we find the ranges of metric parameters and coupling coefficients for which classical timelike singularities in these spacetimes are healed quantum mechanically.
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ABSTRACT: We consider a Dirac field on a $(1 + 2)$-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in $(1+3)$ dimensions, essential self-adjointness on $C_0^{\infty}(r_+,\infty)^2$ of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass $\mu$ of the Dirac field and the cosmological radius $l$ holds true. The very presence of a boundary-like behaviour of $r=\infty$ is at the root of this problem. Also, we determine in a complete way qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the $(1 + 2)$-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed. Comment: 19 pages; IOP style
Journal of Physics A Mathematical and Theoretical 07/2010; 44(2011):025202. · 1.77 Impact Factor
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##### Article: 2+1 dimensional magnetically charged solutions in Einstein - Power - Maxwell theory
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ABSTRACT: We obtain a class of magnetically charged solutions in 2+1 dimensional Einstein - Power - Maxwell theory. In the linear Maxwell limit, such horizonless solutions are known to exist. We show that in 3D geometry, black hole solutions with magnetic charge does not exist even if it is sourced by power-Maxwell field. Physical properties of the solution with particular power k of the Maxwell field is investigated. The true timelike naked curvature singularity develops when k>1 which constitutes one of the striking effects of the power Maxwell field. For specific power parameter k, the occurrence of timelike naked singularity is analysed in quantum mechanical point of view. Quantum test fields obeying the Klein - Gordon and the Dirac equations are used to probe the singularity. It is shown that the class of static pure magnetic spacetime in the power Maxwell theory is quantum mechanically singular when it is probed with fields obeying Klein-Gordon and Dirac equations in the generic case.
Physical review D: Particles and fields 03/2011;

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Aug 7, 2014