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

TL;DR

This paper explores the connection between the Bekenstein-Hawking area-entropy relation and a $D_0$ brane gas model within Yang's quantized space-time algebra, proposing a unified understanding of black hole thermodynamics.

Contribution

It introduces a scheme linking black hole entropy to a $D_0$ brane gas model using Yang's algebra, suggesting a universal relation and a new ansatz relating brane mass and Hawking temperature.

Findings

Relation between area-entropy and brane gas model clarified.

Effective brane mass and Hawking temperature are comparable.

Area-entropy relation slightly shifted from 1/4 due to new ansatz.

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 $1/4.$