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

TL;DR

This paper derives exact analytical expressions for the greybody factor and the decay behavior of a scalar field in a specific Hořava-Lifshitz black hole, enhancing understanding of this gravity theory.

Contribution

It provides the first exact solutions for scalar field propagation and greybody factors in a Hořava-Lifshitz black hole background.

Findings

Exact expression for the greybody factor valid at all frequencies

Scalar perturbations decay monotonically without oscillations

Improved understanding of scalar dynamics in Hořava-Lifshitz gravity

Abstract

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.