Black Hole Entropy from indistinguishable quantum geometric excitations

In loop quantum gravity, the quantum geometry of a black hole horizon consist of discrete non-perturbative quantum geometric excitations (or punctures) labeled by spins, which are responsible for the quantum area of the horizon. If these punctures are compared to a gas of particles, then the spins associated with the punctures can be viewed as single puncture area levels analogous to single particle energy levels. Consequently, if we {\it assume} these punctures to be {\it indistinguishable}, the microstate count for the horizon resembles that of Bose-Einstein counting formula for gas of particles. For the Bekenstein-Hawking area law(BHAL) to follow from the entropy calculation in the large area limit, the Barbero-Immirzi parameter($\g$) approximately takes a constant value.