2013/04/30 by Sho Tanaka
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1140/epjp/i2014-14011-9
published as Eur.Phys.J.Plus(2014)129:11 · 20 pages, punctuation errors corrected and minor modification in English xplanation. arXiv admin note: substantial text overlap with arXiv:1102.3448, arXiv:1006.2885, arXiv:0905.1446
arxiv created 2014/01/27 · arxiv updated 2014/01/28
In confrontation with serious and fundamental problems towards ultimate theory of quantum gravity and physics of Planck scale, 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 \it 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 definite proportional relation, nL\rm dof (VdL)= \cal A (VdL) / Gd, between the number of spatial degrees of freedom nL\rm dof (VdL) inside of any d-dimensional spherical volume VdL with radius L and its boundary area \cal A (VdL). 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: \it Statistical and \it substantial understanding of area-entropy law of black holes under a novel concept of noncommutative quantized space-time.