In the attempts toward a quantum gravity theory, general relativity faces a serious difficulty since it is non-renormalizable theory. Hov{r}ava-Lifshitz gravity offers a framework to circumvent this difficulty, by sacrificing the local Lorentz invariance at ultra-high energy scales in exchange of power-counting renormalizability. The Lorentz symmetry is expected to be recovered at low and medium energy scales. If gravitation is to be described by a Hov{r}ava-Lifshitz gravity theory there are a number of issues that ought to be reexamined in its context, including the question as to whether this gravity incorporates a chronology protection, or particularly if it allows Godel-type solutions with violation of causality. We show that Hov{r}ava-Lifshitz gravity only allows hyperbolic Godel-type space-times whose essential parameters $m$ and $omega$ are in the chronology respecting intervals, excluding therefore any noncausal Godel-type space-times in the hyperbolic class. There emerges from our results that the famous noncausal Godel model is not allowed in Hov{r}ava-Lifshitz gravity. The question as to whether this quantum gravity theory permits hyperbolic Godel-type solutions in the chronology preserving interval of the essential parameters is also examined. We show that Hov{r}ava-Lifshitz gravity not only excludes the noncausal Godel universe, but also rules out any hyperbolic Godel-type solutions for physically well-motivated perfect-fluid matter content.
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