Holographic Relation in Yang's Quantized Space-Time Algebra and Area-Entropy Relation in $D_0$ Brane Gas System. II

Abstract

We investigate a possible inner relation between the familiar Bekenstein-Hawking area-entropy relation and ours presented in a simple $D_0$ brane gas model on the basis of the kinematical holographic relation [KHR] in the Yang's quantized space-time algebra (YSTA). We find out that the relation between them is well understood through the idea of an {\it elementary} Schwarzschild black hole realized on a single $[site]$ of Planckian scale in our scheme. Related arguments possibly explain the origin of a certain kind of universality as seen in $\eta =1/4$ in the Bekenstein-Hawking relation and lead us to notice the similarity between the effective mass of $D_0$ brane, $\mu_S,$ inside black holes and the Hawking radiation temperature, $T_{H.R.} ( = 1/(8\pi M_S) )$, both inversely proportional to the black hole mass $M_S$ and having almost the same order of magnitude. Motivated by this fact, we introduce in our scheme an ansatz which enables us self-consistently to equate $\mu_S$ to $T_{H.R.}$ and leads us to an area-entropy relation with $\eta$ slightly shifted from $1/4.$