Cardy-Verlinde Formula for an Axially Symmetric Dilaton-axion Black Hole

It is shown that the Bekenstein-Hawking entropy of an axially symmetric dilaton-axion black hole can be expressed as a Cardy-Verlinde formula. By utilizing first order correction in the Bekenstein-Hawking entropy we find the modified the expressions for the Casimir energy and pure extensive energy. The first order correction to the Cardy-Verlinde formula in the context of dilaton-axion black hole are obtained with the use of modified cosmic and pure extensive energies.     

Casimir Effect Under Two Dimensional Black Hole Spacetime Background with Global Monopole

A thin layer of the event horizon vicinity to the two-dimension black hole with a global monopole is considered as a system of the Casimir type. The energy-momentum tensor is derived in Boulware vacuum, Hartle-Hawking vacuum and Unruh vacuum respectively. The values are derived in the massless scalar field which satisfies the Dirichlet boundary conditions. Using the Wald's axioms, the result is got which is the same with the one derived by the usual regularized methods. Meanwhile, the energy, energy density, and pressure acting on the boundaries at the asymptotically flat background also are calculated too, and from the energy, Casimir force is derived. The Casimir energy and Casimir force are compared respectively in the background before and after radiation. PACS: 42.50.Lc.     

Hawking radiation and page curves of the black holes in thermal environment

As realistic objects in the Universe, the black holes are surrounded by complex environment. By taking the effect of thermal environment into account, we investigate the evaporation process and the time evolutions (page curves) of the entanglement entropies of Hawking radiation of various types of black holes. It is found that the black holes with the thermal environments evaporate slower than those without the environments due to the environmental contribution of the energy flux in addition to Hawking radiation. For Schwarzschild black hole and Reissner-Nordström black hole in flat spaces, when the initial temperature of the black hole is higher than the environment temperature, the black holes evaporate completely and the Hawking radiation is eventually purified. For Schwarzschild-AdS black hole, it will evaporate completely and the Hawking radiation is purified when the environment temperature is lower than the critical temperature. Otherwise, it will reach an equilibrium state with the environment and the radiation is maximally entangled with the black hole. Our results indicate that the final state of the black hole is determined by the environmental temperature and the temporal evolution and the speed of the information purification process characterized by the page curve of the Hawking radiation is also influenced by the thermal environment significantly.     

二维静态时空中Dirac场的重正化能动张量和Casimir效应

在一般渐近平直的二维静态黑洞时空中,利用重正化能动张量的一般性质, 对位于两“平行板”间满足Dirichlet条件的无质量Dirac场的重正化能动张量的真空期待值进行了分析和计算, 得到了一般表达式.利用该表达式可以给出各种具体渐近平直二维静态黑洞时空中的相应Casimir力.对于重正化能动张量及Casimir力与真空态定义(包括Boulware 真空态、Hartle-Hawking真空态和Unrum真空态三种情况)、Hawking辐射和反常迹的关系分别进行了讨论，给出了相应的表达式和计算结果. 关键词： 能动张量 Casimir 效应 黑洞 真空态     

CGHS Black Hole Analog Moving Mirror and Its Relativistic Quantum Information as Radiation Reaction

The Callan–Giddings–Harvey–Strominger black hole has a spectrum and temperature that correspond to an accelerated reflecting boundary condition in flat spacetime. The beta coefficients are identical to a moving mirror model, where the acceleration is exponential in laboratory time. The center of the black hole is modeled by the perfectly reflecting regularity condition that red-shifts the field modes, which is the source of the particle creation. In addition to computing the energy flux, we find the corresponding moving mirror parameter associated with the black hole mass and the cosmological constant in the gravitational analog system. Generalized to any mirror trajectory, we derive the self-force (Lorentz–Abraham–Dirac), consistently, expressing it and the Larmor power in connection with entanglement entropy, inviting an interpretation of acceleration radiation in terms of information flow. The mirror self-force and radiative power are applied to the particular CGHS black hole analog moving mirror, which reveals the physics of information at the horizon during asymptotic approach to thermal equilibrium.     

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 Evolution under Double‐trace Deformation

In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where the quantum correction of the entanglement entropy gives the leading contribution. We find that in the large black hole limit the bulk entanglement entropy decreases under the double‐trace deformation which is consistent with the holographic c theorem and in the small black hole limit the bulk entanglement entropy increases under the deformation. We also discuss the minimal area correction.     

Universality of black hole quantum computing

By analyzing the key properties of black holes from the point of view of quantum information, we derive a model‐independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft‐enough in order not to offset the basic properties of the system. We derive model‐independent bounds on some crucial time‐scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time‐scales are of the order of the black hole half‐life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life‐time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life‐time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro‐state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.     

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.     

A divergent volume for black holes calls for no ‘firewall’

The presumption that Hawking radiations are thermally distributed can be considered to result from their entanglement with the internal degrees of freedom for a black hole. This leads to the‘firewall' paradox if unitary evolution continues into Page's time when a black hole evaporates away half of its initial entropy. However, if the interior of a black hole houses sufficient degrees of freedom to maintain entanglement with the outside at all times, unitarity can be preserved during the complete radiation process and no firewall will be required. This paper proposes a scenario that rescinds the firewall by introducing the concept of volume for a black hole. Based on the operational definition by Christodoulou and Rovelli(Christodoulou and Rovelli 2015 Phys. Rev. D 91 064046), we show that the volume and its associated entropy for a collapsed black hole diverges if the final evaporation stage is treated using noncommutative space. This implicates the interior of a black hole possesses adequate space to store information for a black hole of any mass, like the inside of a ‘magician's bag’.     

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.     

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.     

Entangled quantum fields near the event horizon and entropy

By fully exploiting the existence of the unitarily inequivalent representations of quantum fields, we exhibit the entanglement between inner and outer particles, with respect to the event horizon of a black hole. We compute the entanglement entropy and we find that the non-unitarity of the mapping, between the vacua in the flat and the curved frames, makes the entanglement very robust.     

On hidden symmetries of extremal Kerr–NUT–AdS–dS black holes

It is well known that the Kerr–NUT–AdS–dS black hole admits two linearly independent Killing vectors and possesses a hidden symmetry generated by a rank-2 Killing tensor. The near-horizon geometry of an extremal Kerr–NUT–AdS–dS black hole admits four linearly independent Killing vectors, and we show how the hidden symmetry of the black hole itself is carried over by means of a modified Killing–Yano potential which is given explicitly. We demonstrate that the corresponding Killing tensor of the near-horizon geometry is reducible as it can be expressed in terms of the Casimir operators formed by the four Killing vectors.     

Gibbons-Maeda dilaton 黑洞的纠缠熵

按纠缠熵方法，计算了Gibbons-Maeda(G-M)dilaton黑洞视界外部与黑洞内量子态纠缠的一薄层内量子场的统计熵，得到了G-M dilaton黑洞的Bekenstein-Hawking熵.用广义不确定原理对量子态密度进行修正，克服了brick-wall模型中视界附近态密度的发散困难，该薄层可以紧贴在事件视界上.对brick-wall外部量子场中与黑洞内自由度有关联的自由度统计熵进行了计算，并把结果与brick-wall内量子场的熵进行比较分析，显示两结果具有与视界面积成正比的一致性，但后者能更 关键词： 纠缠熵 黑洞 广义不确定原理 截断     

Negative Entropy and Black Hole Information

Based on negative entropy in entanglement, it is shown that a single-system Copenhagen measurement protocol is equivalent to the two-system von Neumann scheme with the memory filling up the system with negative information similar to the Dirac sea of negative energy. After equating the two quantum measurement protocols, we then apply this equivalence to the black hole radiation. That is, the black hole evaporation corresponds to the quantum measurement process and the two evaporation approaches, the observable-based single-system and the two-system entanglement-based protocols, can be made equivalent using quantum memory. In particular, the measurement choice θ with the memory state inside the horizon in the entanglement-based scheme is shown to correspond to the observable of the measurement choice θ outside the horizon in the single-system protocol, that is, $\mathcal{O}_{\theta}^{\mathrm{out}} = Q_{\theta}^{\mathrm{in}}$ . This indicates that the black hole as quantum memory is filling up with negative information outside the horizon, and its entropy corresponds to the logarithm of a number of equally probable measurement choices. This shows that the black hole radiation is no different than ordinary quantum theory.     

Black Hole Thermodynamics, Casimir Effect and Induced Gravity

An analogy between the subtraction procedure in the Gibbons-Hawking Euclidean path integral approach to black hole thermodynamics and the Casimir effect is shown. Then a conjecture about a possible Casimir nature of the Gibbons-Hawking subtraction is made in the framework of Sakharov's induced gravity. In this framework it appears that the degrees of freedom involved in the Bekenstein-Hawking entropy can be naturally identified with zero-point modes of the matter fields. Some consequences of this view are sketched.     

Particle creation by a black hole as a consequence of the Casimir effect

It is shown that the effect of particle creation by a black hole is a consequence of the Casimir effect for a spherical shell. The temperature of black-body radiation coincides with that obtained by Hawking.     

The Quantum Entanglement in the Back Ground of Gauss-Bonnet Gravity for a Generically Entangled State

In this work the Hawking-Unruh effect on the quantum entanglement of bosonic field in background of a spherically symmetric black hole of Gauss-Bonnet gravity is investigated beyond the single mode approximation. The entanglement decreases due to Hawking-Unruh effect. However, it has been shown that the dimensions of space time, Gauss-Bonnet term and the parameter β of initial entangled state would be influenced on this degradation. In our investigation, we consider the accelerated observer either near or far from the event horizon and inspect entanglement degradation for them. The mutual information of this bosonic system is also calculated in beyond the single mode approximation and we show that the mutual information will have different behavior when the Hawking temperature increases.