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

摘要

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