Exploring plasma and dark matter on photon deflection by Reissner–Nordström black hole with scalar hair and its shadow

This work aims to study light rays in a Reissner–Nordström black hole with scalar hair (RNBHSH) using the optical metric of the corresponding black hole within the Gauss–Bonnet theorem. Specifically, we first show how spacetime affects the Gaussian optical curvature, and then we determine the light deflection using the technique introduced by Gibbons–Werner. Our analysis of light deflection shows how the electrically charged parameter affects light deflection. We also show the effect of non-magnetized plasma and dark matter on photon trajectories by the RNBHSH. The Event Horizon Telescope has observed the image of a supermassive black hole. Simulation images of RNBHSH were created using a general relativistic ray tracing approach and shadow to complement these scientific investigations. The RNBHSH contains physically attractive image structures, which include shadows of different sizes in their non-magnetized plasma. The ray-tracing technique is used to study the trajectory of photons and null-geodesics around the RNBHSH, and we compute the shadow under non-magnetized impact. Moreover, we analyze the energy emission rate as a function of photon frequency for the given black hole.