Exploring light deflection and black hole shadows in Rastall theory with plasma effects

In this article, we examine the gravitational deflection of particles in curved spacetime immersed in perfect fluid in the context of Rastall theory. We propose an infinite region approach to Gibbons-Werner to avoid singularity, given that the integral region is generally infinite. In the Rastall theory framework, the black hole solutions in the dust field are studied. Additionally, we check the deflection angle from this spacetime under the influence of plasma. Furthermore, we analytically compute plasma's impact on a black hole shadow using a ray-tracing approach and Hamiltonian equation. Hence, the light ray motion equations are independent of the plasma's velocity. It is assumed that plasma is a dispersive medium, pressureless and non-magnetised, and the plasma particle density corresponds to particle accumulation. The supermassive black hole's shadow and emitted energy are explored when plasma falls radially from infinity onto the black hole.