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

TL;DR

This work develops an exact static, spherically symmetric black hole solution in $F(R)$ gravity coupled to ModMax nonlinear electrodynamics in the presence of a cloud of cosmic strings. It provides analytic expressions for the photon sphere and the shadow radius, illustrating how ModMax coupling, $F(R)$ corrections, and string-like matter modify spacetime and null geodesics. The results show that the shadow size increases with the ModMax parameter $\gamma$, the $F(R)$-derivative $f_{R_{0}}$, and the CS parameter $\alpha$, while electric charge $q$ tends to shrink the shadow, with $\alpha$ exerting a particularly strong influence. These findings imply potential observational signatures in BH shadow measurements that could help test modified gravity and cosmic-string environments, and motivate future work on quasinormal modes, energy emission rates, and thermodynamic geometry of these spacetimes.

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.

Figures (3)

• Figure 1: A comparison of the metric function $g(r)$ for different BHs. Here, we set $m_0=1,\gamma=0.5,f_{R_0}=0.9=q,R_0=-0.01$ and $\alpha=0.3$
• Figure 2: Plot of shadow radius $R_{s}$ for different values of BH parameters. Here, we set $M=1$ and $R_0=-0.01$.
• Figure 3: BH shadow in the celestial plane for different values of BH parameters. Here, we set $m_0=1$ and $R_0=-0.01$.