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

Abstract

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 $1/4.$

25 pages, minor typos corrected, several sentences added and improved in sections 2.1, 2.2. 3.1 and the final section 5. arXiv admin note: substantial text overlap with arXiv:1006.2885

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• Five Problems in Quantum Gravity
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Cited by in corpus (1)

• Where Does Black Hole Entropy Lie? Some Remarks on Area-Entropy Law, Holographic Principle and Noncommutative Space-Time