Extremal black hole entropy from conformal string sigma model

We present a string-theory derivation of the semiclassical entropy of extremal dyonic black holes in the approach based on the conformal sigma model (NS-NS embedding of the classical solution). We demonstrate (resolving some puzzles existing in previous related discussions) that the degeneracy responsible for the entropy is due to string oscillations in four transverse dimensions ‘intrinsic’ to the black hole: four non-compact directions of the D = 5 black hole case and three non-compact and one compact (responsible for embedding of magnetic charges) dimensions in the D = 4 black hole case. Oscillations in other compact internal dimensions give subleading contributions to statistical entropy in the limit when all charges are large. The dominant term in the statistical entropy is thus universal (i.e. is the same in type II and heterotic string theory) and agrees with the Bekenstein-Hawking expression.     

On EVH black hole solution in heterotic string theory

We study the near horizon geometry of charged rotating black holes in toroidal compactifications of heterotic string theory. We analyze the extremal vanishing horizon (EVH) limit for these black hole solutions and we will show that the near horizon geometry develops an AdS₃ throat. Furthermore, we will show that the near horizon limit of near EVH black holes has a BTZ factor. We also comment on the CFT dual to this near horizon geometry.     

Microscopic and macroscopic entropy of extremal black holes in string theory

It has been observed on a number of occasions that complex transformations, of real solutions of the field equations to other real solutions, often preserve certain properties of the Weyl tensor. That is, the Petrov type and/or gravito-electromagnetic (GEM) properties of the Weyl tensor are preserved. In this context, we present an outstanding example of a complex windmill transformation of a static (non-physical) anisotropic fluid spacetime of Petrov type $I(M^+)$ that maps to a purely magnetic (PM) spacetime of Petrov type $I(M^{\infty })$ . The PM spacetime is analyzed and compared to the Arianrhod–Lun–McIntosh–Perjés spacetime. It is shown that these spacetimes, although similar in some aspects, are distinct solutions. The main distinction is that the generated PM spacetime satisfies all the standard energy-conditions. This intriguing but purely mathematical scenario may have implications in the area of GEM duality.     

Does string theory solve the puzzles of black hole evaporation?

We point out that the massive modes of closed superstring theories may play a crucial role in the last stages of black hole evaporation. If the Bekenstein-Hawking entropy describes the true degeneracy of a black hole — implying loss of quantum coherence and the unitary evolution of quantum states-it becomes entropically favorable for an evaporating black hole to make a transition to a state of massive string modes. This in turn may decay into massless modes of the string (radiation) avoiding the naked singularity exposed by black hole evaporation in the semiclassical picture. Alternatively, quantum coherence may be maintained if the entropy of an evaporating black hole is much larger than that given by the Bekenstein-Hawking formula. In that case, however, the transition to massive string modes is unlikely. String theories might thus resolve the difficulty of the naked singularity, but it appears likely that they will still involve loss of quantum coherence.This essay received the first award from the Gravity Research Foundation for the year 1986 — Ed.     

Finite entropy of Schwarzschild anti-de sitter black hole in different coordinates

This paper studies the finite statistical-mechanical entropy of the Schwarzschild anti-de Sitter (AdS) spacetime arising from quantum massless scalar field by using the `brick wall' approach in the Painlev\'e and Lemaitre coordinates. At first glance, it seems that the results would be different from that in the Schwarzschild-like coordinate since both the Painlev\'e and the Lemaitre spacetimes do not possess the event horizon obviously. However, this paper proves that the entropies in these coordinates are exactly equivalent to that in the Schwarzschild-like coordinate.     

正则黑洞熵

应用隧道效应所得到的能量谱计算配分函数,进而计算黑洞熵.当本结论取一级近似时,熵修正的对数项与考虑广义不确定关系对黑洞熵修正的对数项一致,然而在计算中没有不确定因子.虽然对数修正项前的因子与考虑热波动对黑洞熵修正中对数项前的因子相同,但所给结论中当黑洞的热容量为负时也不存在发散项.所以本结论具有普遍性. 关键词： 广义不确定关系 热波动 正则系综 量子修正     

Two dimensional black hole entropy

In this paper we consider the two dimensional black hole and use Wald’s formula to find its entropy. Also we consider higher derivative terms. We discuss the case of a massless black hole and find its free energy.     

Universal canonical black hole entropy

Nonrotating black holes in three and four dimensions are shown to possess a canonical entropy obeying the Bekenstein-Hawking area law together with a leading correction (for large horizon areas) given by the logarithm of the area with a universal finite negative coefficient, provided one assumes that the quantum black hole mass spectrum has a power-law relation with the quantum area spectrum found in nonperturbative canonical quantum general relativity. The thermal instability associated with asymptotically flat black holes appears in the appropriate domain for the index characterizing this power-law relation, where the canonical entropy (free energy) is seen to turn complex.     

Tachyon condensation and black hole entropy

String propagation on a cone with deficit angle 2pi(1-1 / N) is considered for the purpose of computing the entropy of a large mass black hole. The entropy computed using the recent results on condensation of twisted-sector tachyons in this theory is found to be in precise agreement with the Bekenstein-Hawking entropy.     

Black hole quantum tunnelling and black hole entropy correction

The Parikh–Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is investigated once more in this work. The first order correction, the log-corrected entropy-area relation, emerges naturally in the tunnelling picture if we consider the emission of a spherical shell. The second order correction to the emission rate for the Schwarzschild black hole is also calculated. At this level, the entropy of the black hole will contain three parts: the usual Bekenstein–Hawking entropy, a logarithmic term and an inverse area term. We find that the coefficient of the logarithmic term is −1. Thus, apart from a coefficient, our correction to the black hole entropy is consistent with that calculated in loop quantum gravity.     

Self-gravitating strings and string/black hole correspondence

In a recent essay, we discussed the possibility of using polymer sizing to model the collapse of a single, long excited string to a black hole. In this letter, we apply this idea to bring further support to string/black hole correspondence. In particular, we reproduce Horowitz and Polchinki's results for self-gravitating fundamental strings and speculate on the nature of the quantum degrees of freedom of black holes in string theory.     

Generalized uncertainty principle and black hole entropy

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this Letter, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction terms of entropy, temperature and energy caused by the generalized uncertainty principle. We calculate Cardy–Verlinde formula after considering the correction. In our calculation, we only think that the Bekenstein–Hawking area theorem is still valid after considering the generalized uncertainty principle and do not introduce any assumption. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the corrections caused by the generalized uncertainty principle to the black hole thermodynamic quantity of the complicated spacetime.     

Barriola-Vilenkin黑洞的统计熵

利用量子统计方法 ,直接计算Barriola_Vilenkin黑洞背景下玻色场和费米场的配分函数 ,然后利用砖墙膜模型计算和讨论黑洞背景下玻色场和费米场的熵     

Kerr-Newman黑洞的统计熵

避开求解黑洞背景下波动方程的困难,应用量子统计方法,直接求解轴对称KerrNewman黑洞背景下Bose场和Fermi场的配分函数.然后利用改进的brickwall方法膜模型,计算黑洞背景下Bose场和Fermi场的熵.得到黑洞熵与视界面积成正比的结论.在所得结论中不存在对数发散项与舍去项,也不存在黑洞视界外标量场或Dirac场为什么是黑洞熵疑难,并且给出粒子的自旋简并度对黑洞熵的影响.为研究各种复杂黑洞熵提供了简捷的途径. 关键词： 量子统计 brick-wall方法 膜模型 黑洞熵     

黑洞的统计熵

运用量子统计的方法,直接求解Schwarzschild时空背景下玻色场和费米场的配分函数,得到熵的积分表达式.按照最近的研究结果,认为黑洞的Hawking辐射过程是隧道效应过程,在考虑黑洞隧道效应产生过程中黑洞能量发生变化的基础上,给出积分的下限为黑洞的视界位置.由此得到黑洞熵的主要项为视界面积的1/4.不存在使人疑惑的紫外截断因子,并且由此可得黑洞辐射粒子的能量与辐射温度成正比的结论. 关键词： 黑洞熵 量子统计 隧道效应 反作用     

Quantum aspects of black hole entropy

This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based N=2 supergravity are also discussed, albeit more briefly.