Abstract
We prove the consistency of the G\"odel 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.
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