Quantum and classical areas of black hole thermodynamics

TL;DR

This paper derives an entropy formula for black holes in loop quantum gravity that is proportional to the classical area and includes a logarithmic correction, ensuring entropy additivity in both U(1) and SU(2) frameworks.

Contribution

It presents a new derivation of black hole entropy proportional to the classical area with a logarithmic correction, maintaining additivity in different gauge formulations.

Findings

Entropy proportional to classical area k with logarithmic correction

Consistency with entropy additivity in U(1) and SU(2) formulations

Addresses issues with previous area eigenvalue-based calculations

Abstract

Most calculations of black hole entropy in loop quantum gravity indicate a term proportional to the area eigenvalue A with a correction involving the logarithm of A. This violates the additivity of the entropy. An entropy proportional to A, with a correction term involving the logarithm of the classical area k, which is consistent with the additivity of entropy, is derived in both U(1) and SU(2) formulations.