Influence of primary hair and plasma on intensity distribution of black hole shadows

In this paper, we investigate the influence of primary hair (l) on the shadows of hairy Schwarzschild and Reissner-Nordström black holes obtained through gravitational decoupling. In the context of hairy Schwarzschild black holes, l either has no effect or consistently enlarges the photon sphere radius. Notably, even when it violates the strong energy condition, it can decrease the radius. For Reissner-Nordström black holes, an additional matter field consistently expands the photon sphere radius, potentially reaching 3M, akin to the pure Schwarzschild case. Remarkably, we demonstrate that black holes can exist even when overcharged (\(Q^2> M^2\)), casting shadows. Specific intensity calculations reveal l consistently reduces it in both scenarios. Furthermore, we investigate the impact of pressureless plasma, finding l exerts a stronger influence on visible size than plasma. These results can help in our understanding of theoretical models of black hole shadows and can be tested by comparison with the images obtained by EHT collaboration.