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

Details Kinematical Holographic Relation in Yang's Quantized Space-Time and Area-Entropy Relation in $D_0$ Brane Gas System Kinematical Holographic Relation in Yang's Quantized Space-Time and Area-Entropy Relation in $D_0$ Brane Gas System

2011-02-16

arxiv.org/abs/1102.3448v2

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, minor typos corrected, several sentences added and improved in sections 2.1, 2.2. 3.1 and the final section 5. arXiv

Scientific paper

We investigate the possible inner relation between the familiar Bekenstein-Hawking area-entropy relation and ours presented in a simple $D_0$ brane gas system on the basis of the kinematical holographic relation [KHR] in the Yang's quantized space-time. We find out that the relation between them is well understood through the idea of {\it elementary} Schwarzschild black hole realized on a single $[site]$ of Planckian scale in our scheme. Related arguments 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 attempt to examine further the physical implication of $\eta$ by introducing in our scheme an ansatz which enables us self-consistently to equate $\mu_S$ to $T_{H.R.}$ and leads us to $\eta$ slightly shifted from $1/4.$

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