https://doi.org/10.1140/epjp/i2014-14011-9
Regular Article
Where does black-hole entropy Lie?
Some remarks on area-entropy law, holographic principle and noncommutative space-time
Kurodani 33-4, Sakyo-ku, 606-8331, Kyoto, Japan
* e-mail: st-desc@kyoto.zaq.ne.jp
Received:
15
August
2013
Accepted:
3
January
2014
Published online:
27
January
2014
In confrontation with serious and fundamental problems towards ultimate theory of quantum gravity and Planck scale physics, we emphasize the importance of underlying noncommutative space-time such as Snyder’s or Yang’s Lorentz-covariant quantized space-time. The background of Bekenstein-Hawking’s area-entropy law and holographic principle is now substantially understood in terms of Kinematical Holographic Relation (KHR), which holds in Yang’s quantized space-time as the result of the kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry. KHR implies a proportional relation, 
, between the number of spatial degrees of freedom 
inside any d -dimensional spherical volume 
with radius L and its boundary area 
. It yields a substantial basis for our new area-entropy law of black holes and further enables us to connect “the first law of black hole mechanics” with “the thermodynamics of black holes” towards our final goal: A statistical and substantial understanding of the area-entropy law of black holes under a novel concept of noncommutative quantized space-time.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2014
