Observational Signatures: Shadow cast by the effective metric of photons for black holes with rational non-linear electrodynamics

Abstract: This study explores spherically symmetric non-linear electrodynamics black holes and their effects on light propagation. We derive the governing metric, revealing radial coordinate dynamics within the event horizon. We analyze photon trajectories, finding that increasing magnetic charge expands the horizon and emission range. Furthermore, with the help of the Event Horizon Telescope results, we constrain parameters and emission profiles. Direct emission dominates, while lensing rings play a lesser role. Comparing with Schwarzschild black holes, we observe higher intensity but a wider emission region in non-linear electrodynamics black holes. This work enhances our understanding of modified spacetimes and their impact on black hole properties.