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

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 for $E_0=$ constant. First, we show that the metric for zero cosmological constant and the Power-Maxwell Lagrangian of the form of $\sqrt{\left|F_{\mu \nu }{F}^{\mu \nu }\right|}$, 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.

9 pages one figure. With major revision and singularity analysis is added

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• Three dimensional nonlinear magnetic AdS solutions through topological defects
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• Quantum probes of timelike naked singularities in $2+1-$ dimensional power - law spacetimes
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• A New 2+1 Dimensional Einstein Gravity Solution Coupled to Born-Infeld Electromagnetic Theory without Cosmological Constan
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