We investigate the propagation and evolution for a massless scalar field in the background of $\lambda=1/2$ 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.
Categories: gr-qc hep-th