Entropy of the Schwarzschild black hole to all orders in the Planck length

TL;DR

This paper calculates the quantum entropy of a scalar field around a Schwarzschild black hole, incorporating all-order Planck length corrections from a generalized uncertainty principle, resulting in an area-proportional entropy without cutoff.

Contribution

It introduces a method to compute black hole entropy with all-order Planck length corrections from GUP, avoiding the need for an arbitrary cutoff.

Findings

Entropy is proportional to the horizon area.

All-order Planck length corrections are incorporated.

No cutoff is needed in the calculation.

Abstract

Considering corrections to all orders in the Planck length on the quantum state density from a generalized uncertainty principle (GUP), we calculate the statistical entropy of the scalar field on the background of the Schwarzschild black hole without any cutoff. We obtain the entropy of the massive scalar field proportional to the horizon area.