Shadow analysis of an approximate rotating black hole solution with weakly coupled global monopole charge

We investigate the shadow properties of a rotating black hole with a weakly coupled global monopole charge, using a modified Newman-Janis algorithm. This study explores how this charge and rotational effects shape the black hole's shadow, causal structure, and ergoregions, with implications for distinguishing it from Kerr-like solutions. Analysis of null geodesics reveals observable features that may constrain the global monopole charge and weak coupling parameters within nonminimal gravity frameworks. Observational data from M87* and Sgr A* constrain the global monopole charge and coupling constant to $0 \leq \gamma \lesssim 0.036$ and $-0.2 \lesssim \alpha \leq 0$, respectively.