Shear-free Dust Solution in General Covariant Ho\v{r}ava-Lifshitz Gravity

Understand

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.