Lifshitz scalar, brick wall method, and GUP in Ho\v{r}ava-Lifshitz Gravity

Using the brick wall method, we study statistical entropy for spherically symmetric black holes in Ho\v{r}ava-Lifshitz gravity. In particular, a Lifshitz scalar field is considered in order to incorporate foliation preserving diffeomorphism which eventually gives a modified dispersion relation. Finally, we obtain the area law without UV cutoff for $z>3$, and discuss some of consequences in connection with the generalized uncertainty principle.