Black hole-wormhole transition in (2+1)-dimensional Einstein-anti-de Sitter gravity coupled to nonlinear electrodynamics

In this paper we present two results in (2 + 1) gravity coupled to nonlinear electrodynamics. First we determine the general form of the electromagnetic field tensor in (2 + 1) gravity coupled to nonlinear electrodynamics in stationary cyclic spacetimes. Secondly, we determine a family of exact solutions in (2 + 1) gravity sourced by a nonlinear electromagnetic field. The solutions are characterized by five parameters: mass M, angular momentum J, cosmological constant Lambda, and two electromagnetic charges q(alpha) and q(beta). Remarkably, the solution can be interpreted as a traversable wormhole, provided the fulfillment of certain inequalities by the characteristic parameters; fine-tuning of the cosmological constant leads to an extreme black hole, whereas by switching off one of the electromagnetic charges, we obtain the BafiadosTeitelboim-Zanelli (BTZ) black hole.