Nonlinearly charged black holes: Shadow and Thin-accretion disk

In this paper, we explore the effect of non-linear electrodynamics (NLED) parameters and magnetic charges on various aspects of black holes, like how they bend light, how they emit radiation, and how they appear as a shadow by considering a thin accretion disk model. We initially examine the overall behavior of the photonsphere and the corresponding shadow silhouette under the effects of these parameters. Using the EHT data for Sgr. A* and M87*, we aim to find constraints for $q_m$. Our results indicate that M87* gives better constraints, and as the value of $\beta$ is varied to increase, the constrained range for $q_m$ widens. At lower values of $q_m$, we find that the shadow radius is close to the observed value. Then, we study different things like how much energy the black hole emits, the temperature of the disk around it, and the kind of light it gives off. We also look at how the black hole shadow appears in different situations. We also study how matter falls onto the black hole from all directions. Finally, we investigate how the magnetic charge affects all these things when we take into account a theory called NLED along with gravity. This study helps us understand the complex relationship between magnetic charge and black holes.