An area rescaling ansatz and black hole entropy from loop quantum gravity

TL;DR

This paper proposes a rescaled area spectrum in loop quantum gravity considering horizon renormalization, deriving black hole entropy without arbitrary parameter choice, and determining the Barbero-Immirzi parameter through physical consistency.

Contribution

It introduces a novel area rescaling ansatz accounting for horizon renormalization, enabling entropy calculation without arbitrary parameter tuning in loop quantum gravity.

Findings

The Bekenstein-Hawking area law is recovered without fixing the Barbero-Immirzi parameter.

A unique rescaling function is identified that aligns the entropy with classical expectations.

The Barbero-Immirzi parameter is physically determined by horizon renormalization considerations.

Abstract

Considering the possibility of `renormalization' of the gravitational constant on the horizon, leading to a dependence on the level of the associated Chern-Simons theory, a rescaled area spectrum is proposed for the non-rotating black hole horizon in loop quantum gravity. The statistical mechanical calculation leading to the entropy provides a unique choice of the rescaling function for which the Bekenstein-Hawking area law is yielded without the need to choose the Barbero-Immirzi parameter $(\gamma)$. $\gamma$ is determined by studying the limit in which the `renormalized' gravitational constant on the horizon asymptotically approaches the `bare' value. Unlike the usual, much criticized, practice of choosing $\gamma$ just for the sake of the entropy matching the area law, its value is now rather determined by a physical consistency requirement.