Study of light deflection and shadow from a hairy black hole under the influence of the non-magnetic plasma

Abstract: This article computes the bending angle of a hairy black hole at weak field limits. The Gauss-Bonnet theorem is applied to the Gaussian optical curvature; this gives a way to calculate the hairy black hole light bending angle using the Gibbons and Werner approach. We determine the light's deflection angle under the influence of gravitational decoupling parameters, non-magnetic plasma, and dark matter. Further, using the ray tracing phenomenon, we determine the shadow at which light is deflected when a non-magnetic plasma medium is present. There must exist unstable circular light orbits that can act as limit curves for light rays in a spiral motion. In this manner, the shadow can be calculated for an observer at any distance from the center, and the energy emission rate for the hairy black hole can be studied.