Entropy of (2+1)-dimensional de Sitter black hole to all orders in the Planck length

TL;DR

This paper computes the entropy of a scalar field in (2+1)-dimensional de Sitter space, incorporating all-order Planck length corrections via GUP, resulting in an entropy proportional to the horizon perimeter.

Contribution

It introduces a method to calculate de Sitter black hole entropy including all-order quantum gravity corrections without artificial cutoffs.

Findings

Entropy proportional to horizon perimeter achieved

All-order Planck length corrections included

No artificial cutoff needed in the calculation

Abstract

We calculate the statistical entropy of a scalar field on the background of (2+1)-dimensional de Sitter space without an artificial cutoff considering corrections to all orders in the Planck length from a generalized uncertainty principle (GUP) on the quantum state density. The desired entropy proportional to the horizon perimeter is obtained.