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

TL;DR

This paper explores the connection between the Bekenstein-Hawking black hole entropy and a $D_0$ brane gas model within Yang's quantized space-time, revealing insights into black hole microstates and universal constants.

Contribution

It introduces a novel relation between black hole entropy and $D_0$ brane systems using kinematical holography in Yang's space-time, linking microscopic brane properties to macroscopic black hole features.

Findings

The relation between black hole entropy and brane system is clarified.

Universality of the entropy coefficient $rac{1}{4}$ is explained.

Effective brane mass and Hawking temperature are shown to be comparable.

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 $1/4.$