Holographic Entanglement Entropy of the BTZ Black Hole

We investigate quantum entanglement of gravitational configurations in 3D AdS gravity using the AdS/CFT correspondence. We derive explicit formulas for the holographic entanglement entropy (EE) of the BTZ black hole, conical singularities and regularized AdS₃. The leading term in the large temperature expansion of the holographic EE of the BTZ black hole reproduces exactly its Bekenstein-Hawking entropy S _BH , whereas the subleading term behaves as ln S _BH . We also show that the leading term of the holographic EE for the BTZ black hole can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. This result indicates that black hole EE is not a fundamental feature of the underlying theory of quantum gravity but emerges when the semiclassical notion of spacetime geometry is used to describe the black hole.     

Quantum geometry and entanglement entropy of a black hole

We have studied here black hole entropy in the framework of quantum geometry. It is pointed out that the black hole radiation consistent with Hawking spectrum can be realized as an effect of quantum geometry using a dynamical formalism for diffeomorphism invariance which envisages a discretized unit of time in the Planck scale. This formalism suggests that torsion acts within a quantized area unit (area bit) associated with a loop and this eventually forbids the Hamiltonian constraint to be satisfied for a finite loop size. We assign a spin with torsion in each area bit and entanglement entropy of a black hole is computed in terms of the entanglement entropy of this spin system. We have derived the Bekenstein-Hawking entropy along with a logarithmic correction term with a specific coefficient. Also we have shown that the Bekenstein-Hawking entropy can be formulated in terms of the Noether charge associated with a diffeomorphism invariant Lagrangian.     

Scalar field in massive BTZ black hole and entanglement entropy

In this paper,we investigate the quantum scalar fields in a massive BTZ black hole background.We study the entropy of the system by evaluating the entanglement entropy using a discretized approach.Specifically,we fit the results with a log-modified formula of the black hole entropy,which is introduced by quantum correction.The coefficients of leading and sub-leading terms affected by the mass of graviton are numerically analyzed.     

Entanglement Entropy of Reissner-Nordström Black Hole and Quantum Isolated Horizon

Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH)^§ the entropy of Reissner-Nordström black hole is studied. According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner-Nordström spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner-Nordström spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein-Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states.     

广义测不准关系与三维BTZ黑洞熵

通过应用在量子引力中,由广义测不准关系得出的新的态密度方程,研究三维BTZ背景下黑洞的熵.当取广义测不准关系中引入的,具有Planck量级与空间维数有关的常数λ为特定值时,得到BTZ黑洞Bekenstein-Hawking 熵和修正项.由于利用新的态密度方程,在计算中不存在用brick-wall模型计算黑洞熵时出现的发散项和小质量近似.所得结论,从量子统计力学角度给出了黑洞Bekenstein-Hawking 熵的修正值,使人们对黑洞熵的修正值有更深入的认识. 关键词： 广义测不准关系 量子统计 BTZ黑洞熵     

Entropy correction to stationary black hole via fermions tunneling beyond semiclassical approximation

Recently, fermions tunneling beyond semiclassical approximation from an uncharged static black hole was investigated by Majhi, which was based on the work of Banerjee and Majhi, it was found that the black hole entropy correction can be produced as the quantum effect of a particle is taken into account. In this paper, we further extend this idea to the stationary Kerr black hole to discuss its entropy correction. To get the corrections correctly, the proportionality parameters of quantum corrections of action I _i to the semiclassical action I ₀ in this case are regarded as the inverse of the product of Planck Length and Planck Mass. The result shows that entropy corrections to the stationary black hole also include the logarithmic term and inverse area term in Bekenstein–Hawking entropy beyond semiclassical approximation.     

Moduli and (un)attractor black hole thermodynamics

We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is AdS ₂ × S ² and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen’s entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal non-BPS Kaluza–Klein black hole.     

Entanglement system,Casimir energy and black hole

We investigate the connection between the entanglement system in Minkowski spacetime and the black hole using the scaling analysis. Here we show that the entanglement system satisfies the Bekenstein entropy bound. Even though the entropies of two systems are the same form, the entanglement energy is different from the black hole energy. Introducing the Casimir energy of the vacuum energy fluctuations rather than the entanglement energy, it shows a feature of the black hole energy. Hence the Casimir energy is more close to the black hole than the entanglement energy. Finally, we find that the entanglement system behaves like the black hole if the gravitational effects are included properly.     

Kerr-Newman黑洞的熵修正

基于Majhi等人最近的工作,利用狄拉克方程,在半经典近似外讨论了Kerr-Newman黑洞的熵修正.在单位制G=c=kB=1下,由于普朗克常数与普朗克长度,普朗克质量和普朗克电荷的平方成正比,作用量的量子修正项与半经典项的比例常数被选为(Mrh-Q2/2)-1.结合视界方程的微分形式和黑洞热力学第一定律,本文得到了荷电稳态黑洞的修正熵并发现修正项同样包括Bekenstein-Hawking熵的对数项和倒数项.     

Statistical Entropy of an Acoustic Black Hole in Bose-Einstein Condensates

The entanglement entropy of an acoustic black hole in a Bose-Einstein condensates (BEC) is derived, which is associated with the phonons generated via the Hawking mechanism in a sonic hole. Considering the dispersion relation of a BEC, we recalculate the entanglement entropy of the acoustic black hole by means of statistical method in two limits. We find that the entropy is still proportional to the area of event horizon, but with a coefficient dependent on the infrared cutoff.     

Entropy Function in the Liouville Theory

In this paper we consider 2D Maxwell-dilaton gravity and calculate modified entropy due to higher order terms of the form ∑a _n R ⁿ . We find that, higher order correction decreases the value of the black hole entropy. Then we compare the effect of higher order corrections with effect of Chern-Simons term on the black hole entropy and obtain the expansion coefficient a _n .     

Canonical Entropy and Phase Transition of Rotating Black Hole

Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein-Havcking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole.     

Thermodynamics of Gauss–Bonnet black holes revisited

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norstr?m-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.     

Thermodynamics and phase transition of the Reissner–Nordstr?m black hole surrounded by quintessence

We investigate thermodynamics and phase transition of the Reissner–Nordstr?m black hole surrounded by quintessence. Using thermodynamical laws of black holes, we derive the expressions of some thermodynamics quantities for the Reissner–Nordstr?m black hole surrounded by quintessence. The variations of the temperature and heat capacity with the entropy were plotted for different values of the state parameter related to the quintessence, ω _q , and the normalization constant related to the density of quintessence c. We show that when varying the entropy of the black hole a phase transition is observed in the black hole. Moreover, when increasing the density of quintessence, the transition point is shifted to lower entropy and the temperature of the black hole decreases.     

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.     

Radiation Spectrum and Correction Entropy of (<Emphasis Type="Italic">n</Emphasis>+4)-dimensional Kerr-(A)dS Black Hole

We extend the classical Damour-Ruffini method and discuss Hawking radiation of an (n+4)-dimensional Kerr-(A)dS black hole. We not only derive the radiation spectrum that satisfies the unitary principle but also obtain the correction term of Bekenstein-Hawking entropy.     

引力彩虹时空中Kerr黑洞的熵谱和面积谱

利用黑洞的绝热不变性,研究了引力彩虹时空中Kerr黑洞的熵谱和面积谱.首先,在引力彩虹时空背景下,计算了Kerr黑洞的绝热不变作用量,并将其与玻尔-索末菲量子化条件相结合,给出了黑洞的熵谱.得到的熵谱没有引力彩虹时空本身具有的粒子能量依赖性,且是与经典Kerr黑洞中原始贝肯斯坦熵谱相同的等间距熵谱.然后,根据黑洞热力学第一定律和黑洞熵谱,给出了与原始贝肯斯坦谱不同的面积谱.该面积谱是非等间距的,而且有对黑洞面积的依赖性,但不依赖于探测粒子的能量.面积谱表明,随着黑洞面积的减少,面积间隔逐步变小;当黑洞达到普朗克尺度时,面积量子可降为零.这表示黑洞面积不再减少,黑洞出现辐射剩余.而在忽略色散关系的修正效应或在大黑洞极限下,面积谱的修正项可以忽略,引力彩虹Kerr黑洞面积谱可以回归到原始贝肯斯坦谱.此外,对引力彩虹时空Kerr黑洞的熵进行了讨论,得到了带有面积倒数修正项的黑洞熵,分析了黑洞熵的量子修正与面积谱量子修正的一致性.