The absence of the Kerr black hole in the Ho\v{r}ava-Lifshitz gravity

We show that the Kerr metric does not exist as a fully rotating black hole solution to the modified Ho\v{r}ava-Lifshitz (HL) gravity with ${\mathrm{\Lambda }}_W=0$ and $\lambda =1$ case. We perform it by showing that the Kerr metric does not satisfy full equations derived from the modified HL gravity.