Type-N, shear-free, perfect-fluid spacetimes with a barotropic equation of state

We present the class of Petrov-type N, shear-free, perfect-fluid solutions of Einstein's field equations in which the fluid satisfies a barotropic equation of state p=p(w) and w+p≢0. All solutions are stationary and possess a three- parameter, abelian group of local isometries which act simply transitively on timelike hypersurfaces. Furthermore, there exists one Killing vector parallel to the vorticity vector and another parallel to the four-velocity. This class of solutions is identified as part of a larger class present in the literature.