1102.3448 (Sho Tanaka)

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

Sho Tanaka

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 $1/4.$

View original: http://arxiv.org/abs/1102.3448