Electrically charged regular black holes in nonlinear electrodynamics: Light rings, shadows, and gravitational lensing

Within nonlinear electrodynamics (NED), photons follow null geodesics of an effective geometry, which is different from the geometry of the spacetime itself. Over the last years, several works were dedicated to investigate the motion of photons in the effective geometry of NED-based magnetically charged regular black hole (RBH) solutions. We study the light rings, shadows, and gravitational lensing of the electrically charged RBH solution proposed by Irina Dymnikova (ID), which is a static and spherically symmetric spacetime with a NED source. We show that the shadow associated with the effective geometry can be almost 10% bigger that the one associated with the standard geometry. We also find that the ID solution may mimic the shadow properties of the Reissner-Nordstrom BH, for low-to-extreme values of the electric charge. Besides that, by using the backwards ray-tracing technique, we obtain that ID and Reissner-Nordstrom BH solutions can have a very similar gravitational lensing, for some values of the correspondent electric charges. We also show that the motion of photons in the effective geometry can be interpreted as a nongeodesic curve submitted to a four-force term, from the perspective of an observer in the standard geometry.