The shadow of black holes in $F(R)$-ModMax theory with cosmic strings

Abstract: This work explores the shadow of a black hole within the framework of $F(R)$-ModMax gravity coupled with a cloud of strings. The Einstein field equations are solved for a nonlinear ModMax electromagnetic source in the context of $F(R)$ gravity and a string cloud. From this solution, we obtain analytical expressions for the photon sphere and shadow radii. Our findings reveal that the interplay between nonlinear electrodynamics, $F(R)$ gravity, and the string cloud significantly alters spacetime geometry, leading to distinct dynamical behaviors for test particles while also amplifying the shadow radius. These results underscore the critical role of cosmic strings effects and modified gravity parameters in shaping black hole shadows.