Exploring potential astrophysical applications of black holes in nonlinear electrodynamics

Abstract: Spacetimes arising from nonlinear electrodynamics (NED) are a good laboratory for studying both the nature of regular black holes (RBH) solutions and the imprints of nonlinear electromagnetic fields within this context. Over the past few decades, NED-sourced black hole (BH) spacetimes have attracted considerable attention, but electrically charged RBHs obtained in the so-called $F$ framework have been less addressed in the literature. We consider two members of the h-family of electrically charged, fully RBHs that are solutions to general relativity minimally coupled to NED. Because of their potential astrophysical and astronomical applications, we mainly focus our investigation on the motion of photons and its implications in the shadow radius and gravitational and kinematic redshift, considering the effective geometry followed by photons in NED. For a BH charge-to-mass ratio below some moderate value, there is almost no way to distinguish these members (and likely all members) of the h-family from the Reissner-Nordstr\"om (RN) BH. In its turn, for a BH charge-to-mass ratio above some moderate value, we observe discrepancies in their physical and geometric properties in comparison to those of the RN BH. Furthermore, we also consider observational data for Sagittarius A$^{*}$ and Messier 87$^{*}$ BHs to impose some constraints on the charge-to-mass ratio of the fully RBHs.