Entropy of (1+1)-dimensional charged black hole to all orders in the Planck length

TL;DR

This paper calculates the entropy of a scalar field in a (1+1)-dimensional charged black hole background, incorporating all-order quantum corrections from a generalized uncertainty principle, resulting in an entropy proportional to the Bekenstein-Hawking entropy without adjustable parameters.

Contribution

It provides an exact calculation of black hole entropy to all orders in the Planck length using GUP, without relying on artificial cutoffs or adjustable parameters.

Findings

Entropy is proportional to Bekenstein-Hawking entropy.

No artificial cutoff needed in the calculation.

Entropy is independent of adjustable minimal length parameters.

Abstract

We study the statistical entropy of a scalar field on the (1+1)-dimensional Maxwell-dilaton background without an artificial cutoff considering corrections to all orders in the Planck length from a generalized uncertainty principle (GUP) on the quantum state density. In contrast to the previous results of the higher dimensional cases having adjustable parameter, we obtain an unadjustable entropy due to the independence of the minimal length while this entropy is proportional to the Bekenstein-Hawking entropy.