Duality mappings within three-dimensional nonlinear electrodynamics

In three-dimensional Einstein–Maxwell gravity the electrostatic Bañados–Teitelboim–Zanelli solution and the magnetostatic Hirschmann–Welch solution are connected by a duality mapping. Here we point out that a similar duality mapping exists among circularly symmetric electrostatic and magnetostatic spacetimes, and electric and magnetic stationary solutions, for a nonlinear electrodynamics coupled to three-dimensional Einstein gravity.