Analytical expressions for greybody factor and dynamic evolution for scalar field in Ho\v{r}ava-Lifshitz black hole

We investigate the propagation and evolution for a massless scalar field in the background of $\lambda =1\mathrm{/}2$ Ho\v{r}ava-Lifshitz black hole with the condition of detailed balance. We fortunately obtain an exact solution for the Klein-Gordon equation. Then, we find an analytical expression for the greybody factor which is valid for any frequency; and also exactly show that the perturbation decays without any oscillation. All of these can help us to understand more about the Ho\v{r}ava-Lifshitz gravity.