Fermions Analysis of IR modified Horava-Lifshitz gravity: Tunneling and Perturbation Perspectives

In this paper, we investigate the fermions Hawking radiation and quasinormal modes in infra-red modified Ho$\check{r}$ava-Lifshitz gravity under tunneling and perturbation perspectives.Firstly, through the fermions tunneling in IR modified Ho$\check{r}$ava-Lifshitz gravity,we obtain the Hawking radiation emission rate, tunneling temperature and entropy for the Kehagias-Sfetsos black hole. It is found that the results of fermions tunneling are in consistence with the thermodynamics results obtained by calculating surface gravity.Secondly, we numerically calculate the lowing quasinormal modes frequencies of fermions perturbations by using WKB formulas including the third orders and the sixth orders approximations simultaneously. It turns out that the actual frequency of fermions perturbation is larger than in the Schwarzschild case, and the damping rate is smaller than for the pure Schwarzschild. The resluts of fermions perturbation suggest the quasinormal modes could be lived more longer in Ho$\check{r}$ava-Lifshitz gravity.