Eur. Phys. J. C (2013) 73: 2314
https://doi.org/10.1140/epjc/s10052-013-2314-0

Regular Article - Theoretical Physics

Area spectrum of horizon and black hole entropy

¹ Department of Physics, Waseda University, Okubo 3-4-1, Tokyo, 169-8555, Japan
² Department of Physics, General Education, College of Engineering, Nihon University, Tokusada, Tamura, Koriyama, Fukushima, 963-8642, Japan

^* e-mail: tomo@gravity.phys.waseda.ac.jp

Received: 29 September 2012
Revised: 9 January 2013
Published online: 22 February 2013

Abstract

We calculate the number of degrees of freedom in spin network states related to the general area spectrum in loop quantum gravity based on the ABCK framework. We find that a black hole entropy (the logarithm of the degrees of freedom) is proportional to its area but it provides us with a different value of the Barbero–Immirzi parameter (γ=0.9284… or 0.7274…). It means that one should be careful in choosing the area spectrum when we describe a horizon area in full quantum gravity.