Where Does Black Hole Entropy Lie? Some Remarks on Area-Entropy Law, Holographic Principle and Noncommutative Space-Time

Sho Tanaka

doi:10.1140/epjp/i2014-14011-9

paper

Where Does Black Hole Entropy Lie? Some Remarks on Area-Entropy Law, Holographic Principle and Noncommutative Space-Time

arXiv:1304.6581 · doi:10.1140/epjp/i2014-14011-9

Abstract

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, $n_{dof}^{L} (V_{d}^{L}) = A (V_{d}^{L}) / G_{d}$ , between the number of spatial degrees of freedom $n_{dof}^{L} (V_{d}^{L})$ inside of any $d -$ dimensional spherical volume $V_{d}^{L}$ with radius $L$ and its boundary area $A (V_{d}^{L}) .$ 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.

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

Where Does Black Hole Entropy Lie? Some Remarks on Area-Entropy Law, Holographic Principle and Noncommutative Space-Time

Abstract

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