A Dynamical Solution in Horava-Lifshitz Gravity in the IR limit

Non-stationary null dust in a spherically symmetric spacetime is studied in the context of a general-covariant Horava-Lifshitz theory. The non-minimal coupling to matter is considered in the infrared limit. The aim of this paper is to study whether the collapse of a null dust-like fluid can be a solution of Ho\v{r}ava-Lifshitz theory in the infrared limit. We have shown that the unique possible solution is static. This solution represents a Minkowski spacetime since the energy density is null.