Black hole entropy for the general area spectrum

TL;DR

This paper calculates black hole entropy using the general area spectrum in loop quantum gravity, confirming proportionality to area and deriving new Barbero-Immirzi parameter values larger than previous estimates.

Contribution

It extends black hole entropy calculations to the general area spectrum in loop quantum gravity, providing new parameter values and confirming the area proportionality.

Findings

Entropy proportional to horizon area

New Barbero-Immirzi parameter values obtained

Consistent with previous simplified spectrum results

Abstract

We consider the possibility that the horizon area is expressed by the general area spectrum in loop quantum gravity and calculate the black hole entropy by counting the degrees of freedom in spin-network states related to its area. Although the general area spectrum has a complex expression, we succeeded in obtaining the result that the black hole entropy is proportional to its area as in previous works where the simplified area formula has been used. This gives new values for the Barbero-Immirzi parameter ($\gamma =0.5802... \mathrm{or} 0.7847...$) which are larger than that of previous works.