Non-linear 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 , 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 rs ≠ 0, resembling the ring singularity of the Kerr-Newman spacetime; while if is positive the curvature invariants of the second solution are finite.