General spherically symmetric black bounces within nonlinear electrodynamics

Over the last years, the search of new regular black bounce solutions has drawn a lot of attention by the international community working in gravitation. Indeed, in the era of gravitational wave detections out of binary mergers and of the imaging of the plasma around supermassive black holes, the study of regular solutions has become a common trend given the unique opportunity posed by multimessenger astronomy to test deviations from the Kerr family of solutions. Among them, in this paper, we consider the black bounce paradigm introduced by Simpson and Visser [J. Cosmol. Astropart. Phys. 02 (2019) 042.] and provide a general procedure for reconstructing static spherically symmetric black bounce-type solutions that might interpolate between regular black holes and wormholes. We show that even after imposing some smoothness and flatness conditions on the metric components, additional analysis is required to obtain a well-defined black bounce solution. Then, the corresponding matter Lagrangian is reconstructed by using nonlinear electrodynamics, and the energy conditions are studied.