Gdel-type metrics in Einstein-Aether theory II: nonflat background in arbitrary dimensions

It was previously proved that the Godel-type metrics with flat three-dimensional background metric solve exactly the field equations of the Einstein-Aether theory in four dimensions. We generalize this result by showing that the stationary Godel-type metrics with nonflat background in D dimensions solve exactly the field equations of the Einstein-Aether theory. The reduced field equations are the (D - 1)-dimensional Euclidean Ricci-flat and the (D - 1)-dimensional source-free Maxwell equations, and the parameters of the theory are left free except c(1) - c(3) = 1. We give a method to produce exact solutions of the Einstein-Aether theory from the Godel-type metrics in D dimensions. By using this method, we present explicit exact solutions to the theory by considering the particular cases: (D - 1)-dimensional Euclidean flat, conformally flat, and Tangherlini backgrounds.