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

TL;DR

This paper investigates black hole entropy in Hořava-Lifshitz gravity using the brick wall method with a Lifshitz scalar, revealing an area law without UV cutoff for certain dynamical exponents and exploring links to the GUP.

Contribution

It introduces a Lifshitz scalar field into the brick wall method for Hořava-Lifshitz black holes, deriving an area law without UV cutoff for z > 3 and discussing implications for the GUP.

Findings

Area law obtained without UV cutoff for z > 3

Modified dispersion relation due to Lifshitz scalar

Connections made to the generalized uncertainty principle

Abstract

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.