Nonlinear electrodynamics generalization of the rotating BTZ black hole

Abstract

We obtain two exact solutions of Einstein gravity coupled to nonlinear electrodynamics (NLED) in ($2+1$)-dimensional anti--de Sitter (AdS) spacetime. The solutions are characterized by the mass $M$, angular momentum $J$, cosmological constant or (anti) de Sitter parameter $\mathrm{\ensuremath{\Lambda}}$, and an electromagnetic parameter $Q$, that is related to an electric field in the first solution and to a magnetic charge for the second solution. Depending on the range of the parameters, the solutions admit a charged rotating asymptotically AdS black hole (BH) interpretation or a charged rotating asymptotically AdS traversable wormhole (WH). If the electromagnetic field is turned off, the stationary Ba\~nados-Teitelboim-Zanelli (BTZ) BH is recovered; in such a way that our BH-WH solutions are nonlinear charged generalizations of the stationary BTZ-BH. Moreover, in contrast to the BTZ metric, the derived AdS solutions are singular at certain radius ${r}_{s}\ensuremath{\ne}0$, resembling the ring singularity of the Kerr-Newman spacetime; while if $\mathrm{\ensuremath{\Lambda}}$ is positive the curvature invariants of the second solution are finite.