Horava-Lifshitz gravity and Godel Universe
  We prove the consistency of the G\"{o}del 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. 
C. Furtado, J. R. Nascimento, A. Yu. Petrov, A. F. Santos
hep-th