Vaidya Solution in General Covariant Ho\v{r}ava-Lifshitz Gravity with the Minimum Coupling and without Projectability: Infrared Limit

TL;DR

This study investigates nonstationary radiative spherically symmetric spacetimes in a specific version of Hořava-Lifshitz gravity, concluding that Vaidya's solution does not have an analogue in this theory's infrared limit.

Contribution

It demonstrates the absence of Vaidya's solution in the infrared limit of covariant Hořava-Lifshitz gravity with minimum coupling, contrasting with General Relativity.

Findings

No Vaidya solution analogue in Hořava-Lifshitz gravity

Analysis conducted in post-Newtonian approximation without projectability

Infrared limit considered with null Newtonian prepotential

Abstract

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of {the} Ho\v{r}ava-Lifshitz gravity with the minimum coupling, in the post-newtonian approximation (PPN), without the projectability condition and in the infrared limit. The Newtonian prepotential $\varphi$ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Ho\v{r}ava-Lifshitz Theory (HLT) with the minimum coupling, as we know in the General Relativity Theory (GRT).