  In this paper, we have studied non stationary dust spherically symmetric
spacetime, in general covariant theory ($U(1)$ extension) of the
Ho\v{r}ava-Lifshitz gravity with the minimally coupling and non-minimum
coupling with matter, in the post-newtonian approximation (PPN) in the infrared
limit. The Newtonian prepotential $\varphi$ was assumed null. The aim of this
work is to know if we can have the same spacetime, as we know in the General
Relativity Theory (GRT), in Ho\v{r}ava-Lifshitz Theory (HLT) in this limit. We
have shown that there is not an analogy of the dust solution in HLT with the
minimally coupling, as in GRT.
  Using non-minimum coupling with matter, we have shown that the solution
admits a process of gravitational collapse, leaving a singularity at the end.
This solution has, qualitatively, the same temporal behaviour as the dust
collapse in GRT. However, we have also found a second possible solution,
representing a bounce behavior that is not found in GRT.
