9 pages Latex, Comments are welcome; Thoroughly revised version, reference and acknowledgements sections enlarged, numerical error in final result corrected, no major changes, to appear in IJTP
In this note we have applied directly the Shannon formula for information theory entropy to derive the Black Hole (Bekenstein-Hawking) entropy. Our analysis is semi-classical in nature since we use the (recently proposed [8]) quantum mechanical near horizon mode functions to compute the tunneling probability that goes in to the Shannon formula, following the general idea of [5]. Our framework conforms to the information theoretic origin of Black Hole entropy, as originally proposed by Bekenstein.
从部分光片熵的协变界，我们导出贝肯斯坦界的一个版本：S/M \leq pi x/hbar，其中S，M和x是任何孤立的弱引力系统的熵，总质量和宽度。由于x可以沿任何空间方向测量，因此在薄系统中，边界变得出乎意料地紧。我们的结果完成了旧的熵界的协变界的特殊情况下的识别。因此，光片所展现的信息与几何之间的联系，远比黑洞热力学最初揭示的要普遍得多，但在任何方面都不弱。
Leading Log Corrections to Bekenstein-Hawking Entropy
我们表明，与任何黑洞相关的贝肯斯坦-霍金熵进行对数修正时，小的热力学波动平衡考虑在内。因此，黑洞熵的校正表达式由$S= A/4 - k \ln(A)$给出，其中$A$是视界面积，$k$是取决于特定黑洞的常数。我们把我们的结果应用到BTZ黑洞，其中$k=3/2$，如前所述，以及反德西特-史瓦西和Reissner-Nordstrom黑洞在任意时空维。最后，我们考察了共形场论在黑洞熵及其修正中的作用。
Black hole entropy is a robust prediction of quantum gravity with no established phenomenological consequences to date. We use the Bekenstein-Hawking entropy formula and general-relativistic statistical mechanics to determine the probability distribution of random geometries uniformly sampled in phase space. We show that this statistics (in the limit $\hbar\to 0$) is relevant to large curvature perturbations, resulting in a population of primordial black holes with zero natal spin. In principle, the identification of such a population at LIGO, Virgo, and future gravitational wave observatories…
Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa's Thermofield Dynamics. We then evaluate the von Neumann black hole--environment entropy and notice…
我们探讨了广义Bekenstein界S <= pi Ma的有效性.我们将熵S定义为能量本征值低于M且局域于宽度为a的平坦空间区域的状态数的对数。如果本地化场模式的边界条件是由菲亚特，然后绑定遇到众所周知的困难与负卡西米尔能量和大的物种数，以及新的问题只出现在广义形式。然而，在现实系统中，有限尺寸效应贡献了额外的能量。我们研究了两种不同的模型来估计这种贡献。我们的分析表明，如果相互作用被适当地包括在内，则该束缚是有效的和非平凡的，因此熵S计数相互作用场的束缚态。
Recently, entropy of static supersymmetric black holes in $AdS_6$ was microscopically counted by the topologically twisted index of five-dimensional superconformal field theories. However, the AdS/CFT dictionary states that the partition function of the boundary field theory corresponds to the on-shell action of the bulk quantum gravity. In this paper, we aim to explain the microscopic counting of black hole entropy by the topologically twisted index. We calculate the renormalized on-shell action and show that the on-shell action equals the Bekenstein-Hawking entropy of the supersymmetric blac…
For a quantum pure state in conformal field theory, we generate the Shannon entropy of its coherence, that is, the von Neumann entropy obtained by introducing quantum measurement errors. We give a holographic interpretation of this Shannon entropy, based on Swingle's interpretation of anti-de Sitter space/conformal field theory (AdS/CFT) correspondence in the context of AdS$_3$/CFT$_2$. As a result of this interpretation, we conjecture a differential geometrical formula for the Shannon entropy of the coherence of a quantum pure or purified state in CFT$_2$ at thermal and momentum equilibrium a…
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
