Constraints on charged symmergent black hole from shadow and lensing

In this paper, we report on exact charged black hole solutions in symmergent gravity with Maxwell field. Symmergent gravity induces the gravitational constant G, quadratic curvature coefficient cO , and the vacuum energy VO from the flat spacetime matter loops. In the limit in which all fields are degenerate in mass, the vacuum energy VO can be expressed in terms of G and cO . We parametrize deviation from this limit by a parameter a such that the black hole spacetime is de Sitter (dS) for a<1 and anti-de Sitter (AdS) for a>1 . In our analysis, we study horizon formation, shadow cast and gravitational lensing as functions of the black hole charge, and find that there is an upper bound on the charge. At relatively low values of charge, applicable to astronomical black holes, we determine constraints on cO and a using the Event Horizon Telescope (EHT) data from Sgr. A* and M87*. We apply these constraints to reveal how the shadow radius behaves as the observer distance rO varies. It is revealed that black hole charge directly influences the shadow silhouette, but the symmergent parameters have a tenuous effect. We also explored the weak field regime by using the Gauss-Bonnet theorem to study the weak deflection angle caused by the M87* black hole. We have found that impact parameters comparable to the actual distance D = 16.8 Mpc show the potential detectability of such an angle through advanced astronomical telescopes. Overall, our results provide new insights into the behavior of charged black holes in the context of symmergent gravity and offer a new way to test these theories against observational data.