Nonlinear electrodynamics generalization of the rotating BTZ black hole

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 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 Banados-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) not equal 0, resembling the ring singularity of the Kerr-Newman spacetime; while if Lambda is positive the curvature invariants of the second solution are finite.