On some structure results for Gödel-type spacetimes

For the four dimensional case in particular, we classify the Gödel-type spacetimes with constant vorticity scalar. We give a complete list of the solutions, which provides a generalization of an observation by Gödel, proved later by Ozsváth: The Gödel spacetime and Einstein's static universe are the only stationary Λ-dust solutions of Einstein's equations with positive energy density that are spatially homogeneous.