Horava-Lifshitz gravity and Gödel universe

We prove the consistency of the Gödel metric with the Horava-Lifshitz gravity whose action involves terms with $z=1$, $z=2$, and $z=3$. We show that, for different relations between the parameters of the theory, this consistency is achieved for different classes of matter; in particular, for the small cosmological constant, it is achieved only for the exotic matter—that is, ghosts or phantom matter.