Shadow behavior of an EMSG charged black hole

Abstract: Recent shadow images of Sgr A and M87 captured by Event Horizon Telescope (EHT) collaboration confirms the existence of black holes or their possible alternatives in the center of galaxies. On the other hand, the new image of Sgr A in polarized light suggests a Magnetic field spiraling at the Edge of the Milky Way Central Black Hole. Due to the gravitational lensing effect, the bending of light in the background geometry of the black hole casts a shadow. In recent years, black holes and their properties have been vastly studied in the framework of General Relativity and other modified theories of gravity. One of the possibilities to generalize GR is Energy Momentum Squared Gravity (EMSG). It is important to mention that EMSG modifies all matter field equations, adding some non linear terms to Maxwell equations. EMSG theory as a modified theory of gravity predicts an asymptotically de Sitter charged black hole whose shadow cast and other related characteristics have not been examined yet. Hence we consider the EMSG charged black hole and investigate the shadow shape of this kind of black hole solution in confrontation with EHT results. In the case of non linear electrodynamics, the path of the photon is null on some effective metric. By deriving the effective metric of an EMSG charged black hole we study the null geodesics of the effective metric in the Hamilton Jacobi method. we find the photon orbits and compute the shadow size of this black hole. Then we examine how electric charge and the coupling constant of the EMSG affect the shadow size of the black hole in a positively accelerated expanding universe (with a positive cosmological constant). We explore the viable values of these parameters constrained by EHT data by comparing the shadow radius of an EMSG charged black hole with the shadow size of Sgr A.