In connection with the long saga of the (claimed) microscopic calculations of the Hawking-Bekenstein entropy in (3+1) Loop Quantum Gravity (LQG) and related approaches I have the following question: Ignoring the question of the overall coefficient, what is the most clearly articulated argument that the entropy satisfies an area law in the first place?
For example, in A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, http://arxiv.org/abs/gr-qc/9710007, I read
It is intuitively clear that not all the degrees of freedom described by fields $^\gamma A$, $^\gamma\Sigma$ are relevant to the problem of black hole entropy. In particular, there are ‘volume’ degrees of freedom in the theory corresponding to gravitational waves far away from $\Delta$ which should not be taken into account as genuine black hole degrees of freedom. The ‘surface’ degrees of freedom describing the geometry of the horizon S have a different status. It has often been argued (see, e.g., [3] and references therein) that it is the degrees of freedom ‘living on the horizon’ that should account for the entropy. We adopt this viewpoint in our approach.
This does not really say that the area law can be derived. It only says that the entropy 'should' be dominated by surface degrees of freedom. Are there any papers in the literature in which an area law is derived?
