Impact of non-magnetized plasma on the photon deflection and shadow of a Rastall spacetime in phantom field

In this study, we investigate the photon deflection of spacetime in the phantom field using Rastall’s theory. We suggest an infinite region method for Gibbons–Werner to avoid singularity in the integral region. The Rastall concept structure explores black hole spacetime in the phantom field. Furthermore, we examine the photon deflection of the black hole under the impact of non-magnetized plasma. In addition, we use a ray-tracing technique and the Hamiltonian formula to derive the effects of non-magnetized plasma on a black hole shadow. The light ray equations of motion are independent of the non-magnetized plasma’s velocity. The non-magnetized plasma is considered a dispersive medium with a concentration of particles. The non-magnetized plasma descends radially to infinity onto the black hole, illuminating its shadow and showing radiation. We analyze how characteristics such as metric function parameters and non-magnetized plasma parameters affect the energy emission rate of black holes.