P-Loop Oscillator on Clifford Manifolds and Black Hole Entropy

Abstract

A new relativity theory, or more concretely an extended relativity theory, actively developed by one of the authors incorporated 3 basic concepts. They are the old idea of Chew about bootstrapping, Nottale's scale relativity, and enlargement of the conventional time-space by inclusion of noncommutative Clifford manifolds where all p-branes are treated on equal footing. The latter allowed one to write a master action functional. The resulting functional equation is simplified and applied to the p-loop oscillator. Its respective solution is a generalization of the conventional point oscillator. In addition , it exhibits some novel features: an emergence of two explicit scales delineating the asymptotic regimes (Planck scale region and a smooth region of a conventional point oscillator). In the most interesting Planck scale regime, the solution reproduces in an elementary fashion the basic relations of string theory (including string tension quantization). In addition, it is shown that comparing the massive (super) string degeneracy with the p-loop degeneracy one is arriving at the proportionality between the Shannon entropy of a p-loop oscillator in D-dimensional space and the Bekenstein-Hawking entropy of the black hole of a size comparable with a string scale.