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

TL;DR

This paper presents new solutions in 2+1-dimensional Einstein-Power-Maxwell theory, including a wormhole and a naked singularity, analyzing their properties and quantum nature using scalar and spinor fields.

Contribution

It introduces novel Einstein-Power-Maxwell solutions in 2+1 dimensions, including a wormhole and a naked singularity, with analysis of their quantum properties.

Findings

Derived a wormhole solution with non-zero cosmological constant.

Identified a naked singularity probed by quantum fields.

Connected solutions to scalar field models in 2+1 gravity.

Abstract

We introduce a class of solutions in $2+1-$dimensional Einstein-Power-Maxwell theory for circularly symmetric electric field. The electromagnetic field is considered with an angular component given by $% F_{\mu \nu }=E_{0}\delta_{\mu }^{t}\delta_{\nu }^{\theta }$ for $E_{0}=$ constant. First, we show that the metric for zero cosmological constant and the Power-Maxwell Lagrangian of the form of $\sqrt{\left\vert F_{\mu \nu }F^{\mu \nu }\right\vert }$, coincides with the solution given in $2+1-$% dimensional gravity coupled with a massless, self interacting real scalar field. With the same Lagrangian and a non-zero cosmological constant we obtain a non-asymptotically flat wormhole solution in $2+1-$dimensions. The confining motions of massive charged and chargeless particles are investigated too. Secondly, another interesting solution is given for zero cosmological constant together with conformal invariant condition. The formation of timelike naked singularity for this particular case is investigated within the framework of the quantum mechanics. Quantum fields obeying the Klein-Gordon and Dirac equations are used to probe the singularity and test the quantum mechanical status of the singularity.