Entanglement entropy of black holes and anti-de Sitter space/conformal-field-theory correspondence

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.     

Hawking Radiation from the Higher-Dimensional Schwarzschild de Sitter and Anti-de Sitter Black Holes via Covariant Anomaly

Very recently, a conceptually clean and economical anomaly cancellation method, based on the initial work of Robinson and Wilczek, on Hawking radiation was proposed. On the basis of this formalism, we investigate Hawking radiation from the higher dimensional Schwarzschild de Sitter and Anti-de Sitter black holes. To describe the observable physics in de Sitter space, we construct the effective field theory between the event horizon and cosmological horizon. Our result shows that when the underlying diffeomorphism symmetries are saved at the quantum level, Hawking radiation, from not only the event horizon but also the cosmological horizon in the higher dimensional space time, can be determined by the covariant compensating fluxes of energy momentum tensor. Meanwhile, we also discuss the exact radiation spectrum by incorporating the self-gravitational interaction and back reaction of the outgoing modes.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

Statistical Entropy of Vaidya-de Sitter Black Hole to All Orders in Planck Length

Considering corrections to all orders in Planck length on the quantum state density from generalized uncertainty principle, we calculate the statistical entropy of scalar field near event horizon and cosmological horizon of Vaidya-de Sitter black hole without any artificial cutoff. It is shown that the entropy is linear sum of event horizon area and cosmological horizon area and there are similar proportional parameters related to changing rate of the horizon position. This is different from the static and stationary cases.     

Generalized uncertainty principle and tunnelin gradiation of the SAdS5 black hole

After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a five-dimensional Schwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a two-order small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.     

Schwarzchild-de Sitter 黑洞的热力学性质

在考虑黑洞视界与宇宙视界具有关联性的基础上,证明de Sitter时空的热力学熵为黑洞视界热力学熵与宇宙视界热力学熵之和.给出了考虑两视界具有关联性后的de Sitter时空的热力学特性.研究表明,de Sitter时空的能量上限为纯de Sitter时空能量,deSitter时空的热容量是负的,de Sitter时空一般是量子力学不稳定的.     

Black Hole and Cosmic Entropy for Schwarzschild–de Sitter Space–Time

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method in the background of the Schwarzschild–de Sitter space–time. We obtain the entropy of a black hole and the cosmic entropy at nonasymptotic flat space. When the cut-off satisfies the proper condition, the entropy of a black hole is proportional to the area of a black hole horizon, and the cosmic entropy is proportional to the cosmic horizon area.     

On thermodynamics of RN-dS black hole surrounded by the quintessence

De Sitter black holes have the black hole horizon and the cosmological horizon, and the thermodynamic quantities on the two horizons all satisfy the first law of thermodynamics. The thermodynamic quantities on the two horizons are not independent but are correlated to each other. Taking de Sitter space-time as thermodynamic system, we investigated the effective thermodynamic quantities of Reissner–Nordström de Sitter black hole surrounded by the quintessence (RN-DSQ). We obtained the effective temperature and entropy of the system by considering the corrections between the black hole horizon and the cosmological horizon. We found that the entropy of the RN-DSQ is in agreement with that of Reissner–Nordström de Sitter black hole. It offers a basis for further studying of the thermodynamic properties of de Sitter space-time.     

Acceleration-enlarged symmetries in nonrelativistic space-time with a cosmological constant

By considering the nonrelativistic limit of de Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton–Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian and Hamiltonian framework for constructing models quasi-invariant under enlarged NH symmetries that depend on three parameters described by three nonvanishing central charges. The Hamiltonian dynamics then splits into external and internal sectors with new noncommutative structures of external and internal phase spaces. We show that in the limit of vanishing cosmological constant the system reduces to the one, which possesses acceleration-enlarged Galilean symmetries.     

The Cardy-Verlinde formula and entropyof topological Kerr- Newman black holes in de Sitter spaces

In this paper we show that the entropy of a cosmological horizon in 4-dimensional topological Kerr-Newman-de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any number of dimensions. Furthermore, we find that the entropy of a black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Such results presume a well-defined dS/CFT correspondence, which has not yet attained the credibility of its AdS analogue.Received: 7 April 2003, Revised: 18 June 2003, Published online: 29 August 2003     

Thermodynamics of black holes in anti-de Sitter space

The Einstein equations with a negative cosmological constant admit black hole solutions which are asymptotic to anti-de Sitter space. Like black holes in asymptotically flat space, these solutions have thermodynamic properties including a characteristic temperature and an intrinsic entropy equal to one quarter of the area of the event horizon in Planck units. There are however some important differences from the asymptotically flat case. A black hole in anti-de Sitter space has a minimum temperature which occurs when its size is of the order of the characteristic radius of the anti-de Sitter space. For larger black holes the red-shifted temperature measured at infinity is greater. This means that such black holes have positive specific heat and can be in stable equilibrium with thermal radiation at a fixed temperature. It also implies that the canonical ensemble exists for asymptotically anti-de Sitter space, unlike the case for asymptotically flat space. One can also consider the microcanonical ensemble. One can avoid the problem that arises in asymptotically flat space of having to put the system in a box with unphysical perfectly reflecting walls because the gravitational potential of anti-de Sitter space acts as a box of finite volume.     

Schwarzschild-de Sitter黑洞宇宙视界量子态的熵

采用由广义不确定关系得到的新的态密度方程 ,研究了Schwarzchild deSitter时空背景下黑洞宇宙视界的熵 .利用新的态密度方程 ,克服了用brick wall模型方法计算黑洞熵 ,在消除紫外发散需取截断的不完善之处 ,以此揭示了黑洞熵与其视界面积成正比这一内在联系 ,进一步表明黑洞熵是视界面处量子态的熵     

Quantum statistical entropy for Kerr－de Sitter black hole

Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n 2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole‘s entropy which contains two horizons (a black hole‘s horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole‘s horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole‘s entropy and horizon‘s area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.     

Schwarzschild-de-Sitter黑洞宇宙视界量子态的熵

采用由广义不确定关系得到的新的态密度方程，研究了Schwarzchild-de-Sitter时空背景下黑洞宇宙视界的熵.利用新的态密度方程，克服了用brick wall模型方法计算黑洞熵，在消除紫外发散需取截断的不完善之处，以此揭示了黑洞熵与其视界面积成正比这一内在联系，进一步表明黑洞熵是视界面处量子态的熵. 关键词： 黑洞 广义不确定关系 态密度 熵     

Stability of gravity with a cosmological constant

The stability properties of Einstein theory with a cosmological constant Λ are investigated. For Λ > 0, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For Λ < 0, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressedfor general field hamiltonians. Stability for Λ < 0 is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.     

Entropy of Higher-Dimensional Charged de Sitter Black Holes and Phase Transition

From a new perspective, we discuss the thermodynamic entropy of (n+2)-dimensional Reissner-Nordströmde Sitter (RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this condition, we obtain the extra contribution to the total entropy. With the corrected entropy, we derive other effective thermodynamic quantities and analyze the phase transition of the RNdS black hole in analogy to the usual thermodynamic system.     

Dirac Fields in 3D de Sitter Spacetime

We show that the Dirac equation is separable in the circularly symmetric metric in three dimensions and when the background spacetime is de Sitter we find exact solutions to the radial equations. Using these results we show that the de Sitter horizon has a cross section equal to zero for the massless Dirac field, as in the case of the scalar field. Also, using the improved brick wall model we calculate the fermionic entropy associated with the de Sitter horizon and we compare it with some results previously published.     

Q-Stars in Anti de Sitter Spacetime

We study q-stars with various symmetries in anti de Sitter spacetime in 3+1 dimensions. Comparing with the case of flat spacetime, we find that the value of the field at the center of the soliton is larger when the other parameters show a more complicated behavior. We also investigate their phase space when the symmetry is local and the effect of the charge to its stability.     

利用广义不确定关系计算 Reissner-Nordström-de Sitter黑洞的统计力学熵

利用广义不确定关系修正的态密度方程并采用Wentzel-Kramers-Brillouin (WKB) 近似方法, 计算了Reissner-Nordström-de Sitter (RNdS) 黑洞时空中标量场的统计力学熵. 结果表明, 由这种方法得到的黑洞熵与它的内、外视界面积和宇宙视界面积之和成正比, 这与采用其他方法所得的结果一致, 从而揭示了黑洞熵与视界面积之间的内在联系, 也进一步表明了黑洞熵是视界面上量子态的熵, 是一种量子效应.     

高维de Sitter时空中宇宙视界处的Fermi子隧穿

运用半经典近似理论,本文研究了来自静态高维deSitter时空和高维Schwarzschild-de Sitter时空宇宙视界处的Fermi子隧穿辐射.在文中,描述1/2自旋粒子行为的Dirac方程被简化为一个简单的形式,接着运用方程组有非平凡解的条件,可以得到了半经典的Hamilton-Jacobi方程,从而使得问题大大得以简化,最终得到了静态de Sitter时空中宇宙视界处的Fermi子隧穿率和Hawking温度.