Study of light deflection and shadow in the Rindler-like Schwarzschild solution

In this paper, we calculate the deflection angle in the non-plasma medium by expanding the Keeton–Petters approach. We use analysis to determine how non-magnetic plasma affects the shadow of a Schwarzschild–Rindler black hole. We only consider the spherically symmetric case in which the shadow is circular. It is assumed that the plasma is independent of pressure and magnetization. From a specified spherically symmetric spacetime, we compute the results for a spherically symmetric plasma density. Our main purpose is to derive analytically a formula for the orbital radius of the shadow. Due to the diffusive nature of plasma, the shadow’s radius is influenced by the frequency of the photons. The impacts of the non-magnetic plasma are important in radio establishment. We determine that the non-magnetic plasma incorporates a decreasing impact on the shadow size for a distant observer from the Schwarzschild–Rindler black hole. Moreover, we graphically analyze the impacts of different parameters on the shadow of the corresponding black hole.