Optical Signatures of Einstein-Euler-Heisenberg AdS/dS Black Holes in the light of Event Horizon Telescope

Recent observations of the supermassive black holes $ M87^{*} $ and Sgr A$^{*}$ by the Event Horizon Telescope (EHT) have sparked intensified interest in studying the optical appearance of black holes (BHs). Inspired by this, we carry out a study on the optical features of Einstein-Euler-Heisenberg-Anti de Sitter/de Sitter (EEH-AdS/dS) BHs, including the trajectories of photons, shadow geometrical shape, energy emission rate, and deflection of light in this spacetime. Since, due to the nonlinear electrodynamics effects, photons propagate along null geodesics in an effective metric rather than the background metric, we first derive the effective metric of the EEH-AdS/dS BH. Then we study the null geodesics of the resulting effective metric and eventually compute the size of the EEH-AdS/dS BH shadow. To validate our results, we confront our results with the extracted information from EHT data of the supermassive BHs $ M87^{*} $ and estimate lower bounds for the shadow radius.