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

Abstract

We introduce a class of solutions in 2 + 1-dimensional Einstein-Power-Maxwell theory for a circularly symmetric electric field. The electromagnetic field is considered with an angular component given byFirst, we show that the metric for zero cosmological constant and the Power-MaxwellLagrangian of the form of F μν F μν 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 the conformal invariant condition. The formation of a 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.

Robinson–Trautman solution with nonlinear electrodynamics

“…This solution generalizes the SSS solutions given in [59] where this type of Lagrangian is used for the first time.…”

Nonlinearly charged Lifshitz black holes for any exponent z > 1

“…This kind of power-law Lagrangian has been exhaustively studied in refs. [28][29][30][31][32][33][34][35][36][37][38]. Note that in ref.…”

“…The renewal interest on nonlinear electrodynamics matches with their emergence and importance in the low energy limit of heterotic string theory. Also, nonlinear electrodynamics have been proved to be a powerful and useful tool in order to construct black hole solutions with interesting features and properties as for example regular black holes [23][24][25][26][27] or black holes with nonstandard asymptotic behaviors in Einstein gravity or some of its generalizations [28][29][30][31][32][33][34][35][36][37][38]. Charged black hole solutions emerging from nonlinear theories also have nice thermodynamics properties which make them attractive to be studied.…”

“…In section 4, we analyze in detail a particular case of our (H, P )-electrodynamics with invertible constitutive relations, for which the nonlinear electrodynamics Lagrangian can be written as a single function of the Maxwell invariant of the strength F µν , concretely becoming a power law intensively studied in the recent literature, see e.g. [28][29][30][31][32][33][34][35][36][37][38]. In section 5, we exhaustively study the existence of event horizons for all the values of the parameters.…”

Three dimensional nonlinear magnetic AdS solutions through topological defects

“…In addition, in context of quantum gravity and string theory, also due to AdS/CFT correspondence, these theories play an undeniable important role in describing different phenomena specially in low dimensional spacetime [97][98][99]. Recently, some theories have been proposed for obtaining magnetic solutions in three dimensions and magnetic monopole [100,101].…”