GUP corrected entropy of the Schwarzschild black hole in holographic massive gravity

Abstract

We obtain the statistical entropy of a scalar field on the Schwarzschild black hole in holographic massive gravity by considering corrections on the density of quantum states to all orders in the Planck length from a generalized uncertainty principle (GUP). As a result, we find not only the generalized Bekenstein-Hawking entropy depending on holographically massive gravitons without any artificial cutoff, but also new additional correction terms, which are proportional to surface gravity. Moreover, we also observe that all order GUP corrected entropy is improved to have smaller GUP parameter $\lambda$ than the previous results.