The Statistical Mechanics of Microscopic Long-Range Bulk-Boundary Dependence in Black-Hole Physics and Holography

We argue in the following that the entropy-area law of black-hole physics and the various holographic bounds are the consequences of the microscopic dynamics of elementary degrees of freedom living on or near the Planck scale. We locate them both in the interior and on the boundary of, for example, the black hole with the strange area-behavior of various quantities being the result of a long-range bulk-boundary dependence among these degrees of freedom. In contrast to other approaches we regard the vacuum fluctuations on microscopic scales as the relevant elementary building blocks. In so far certain relations to to old ideas of Sakharov, Zeldovich et al are acknowledged (induced gravity). Most importantly, we prove that the existence of a large energy gap between a few low-lying excitation patterns and the majority of the other (in principle) possible excitation patterns in a subvolume with given boundary excitation is crucial for this area-dependence. We also remark that this is an indication that some particular entangled space-time geometry of a somewhat non-local character prevails in the microscopic (Planck) regime. Our findings are corroborated by the explanation of a number of open questions in the field (see the table of contents at the end of the introduction).