Exact solutions for static spherically symmetric spacetime with a perfect fluid in Rastall theory

In general relativity, exact Liouvillian solutions for a static and spherically symmetric spacetime with a perfect fluid and the equation of state p(r) = wρ(r) are known only for w = 0, -1/6 , -1/5 , -1/3 , and -1. We extend this setup to Rastall theory, presenting the relation between the Rastall parameter and the constant w, and deriving exact solutions that correspond to their known counterparts in general relativity, except for w = -1/6 . Furthermore, we find that, when w ≠ 1/3 , -1, there exist several types of solutions whose behaviors change depending on the choice of constants.