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

TL;DR

This paper explores the holographic relation in Yang's quantized space-time algebra and derives an area-entropy relation for a D0 brane gas system, linking it to black hole entropy in M-theory.

Contribution

It introduces a new kinematical holographic relation in YSTA and derives an area-entropy relation for D0 brane gas systems, connecting noncommutative geometry with black hole physics.

Findings

Derived a kinematical holographic relation in YSTA.

Established an area-entropy relation in D0 brane gas system.

Linked the relation to Bekenstein-Hawking black hole entropy.

Abstract

In the preceding paper, we derived a kind of kinematical holographic relation (KHR) in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). It essentially reflects the fundamental nature of the noncommutative geometry of YSTA and its representation, that is, a definite kinematical reduction of spatial degrees of freedom in comparison with the ordinary lattice space. On the basis of the relation and its extension to various spatial dimensions, we derive a new area-entropy relation in a simple $D_0$ brane gas system subject to YSTA, following the idea of M-theory. Furthermore, we make clear its inner relation with the Bekenstein-Hawking area-entropy relation in connection with Schwarzschild black hole.