G\"odel-type universes and chronology protection in Horava-Lifshitz gravity

Understand

In the attempts toward a quantum gravity theory, general relativity faces a serious difficulty since it is non-renormalizable theory.

• Ho\v{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 Ho\v{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 G\"odel-type solutions with violation of causality.