Minimal model for the Bekenstein-Hawking entropy

Abstract

In this work we derive the Bekenstein-Hawking entropy formula, $S=\frac{A}{4{l}_{p}^{2}}$, from the following minimal assumptions: (i) there is a minimum area, ${A}_{\mathrm{min}}$, proportional to ${l}_{p}^{2}$; (ii) the event horizon area, $A$, is tessellated by $N=A/{A}_{\mathrm{min}}$ distinguishable units; and (iii) the internal structure of these units is that of an infinite tower of internal levels. Although our results are model independent, this internal structure can be realized as the excitations of more fundamental entities such as, for instance, strings or loop quantum gravity spin networks. Even more, once the microstates of the black hole are taken to be singlets formed within the infinite tower of states describing the whole event horizon, the correction term $\ensuremath{-}\frac{3}{2}\mathrm{log}A$ emerges from our model. Finally, some comments regarding the applicability of the present model to extremal black holes, as well as possible relationships with spectral geometry and other approaches are pointed out. Our results are independent of the dimension of the black hole and whether it is rotating or not.