Lifshitz scalar, brick wall method, and generalized uncertainty principle in Hořava-Lifshitz gravity

Abstract

Using the brick-wall method, we study statistical entropy for spherically symmetric black holes in Ho\ifmmode \check{r}\else \v{r}\fi{}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 the UV cutoff for $z>3$ and discuss some of the consequences in connection with the generalized uncertainty principle.