Hawking radiation from a Vaidya black hole by Hamilton-Jacobi method

Using the Hamilton-Jacobi method, Hawking radiation from the apparent horizon of a dynamical Vaidya black hole is calculated. The black hole thermodynamics can be built successfully on the apparent horizon. If a relativistic perturbation is given to the apparent horizon, a similar calculation can also lead to a purely thermal spectrum, which corresponds to a modified temperature from the former. The first law of thermodynamics can also be constructed successfully at a new supersurface which has a small deviation from the apparent horizon. When the event horizon is thought as such a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous result that asserts that thermodynamics should be built on the event horizon. It is concluded that the thermodynamics should be constructed on the apparent horizon exactly while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.     

Where Does Hawking Radiation of a Dynamical Black Hole Come from?

Using the gravitational anomaly method proposed by Robinson and Wilczek, Hawking radiation from the apparent horizon of a Vaidya black hole is calculated. The thermodynamics can be built successfully on the apparent horizon. In the meantime, when a time-dependent perturbation is given to the apparent horizon, the first law of thermodynamics can also be constructed successfully at a new supersurface near the apparent horizon. The expressions of the characteristic position and temperature are consistent with the previous result where the viewpoint is that the thermodynamics should be built on the event horizon. Based on the results, the thermodynamics should be constructed on the apparent horizon exactly while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.     

The thermodynamics in a dynamical black hole

Considering the back-reaction of emitting particles to the black hole, a “new” horizon is suggested where thermodynamics can be built in the dynamical black hole. It, at least, means that the thermodynamics of a dynamical black hole should not be constructed at the original event horizon any more. The temperature, “new” horizon position and radiating particles’ energy will be consistent again under the theory of equilibrium thermodynamical system.      

General Tortoise Coordinate Transformation in a Dynamical Kerr-Newman Black Hole

Under the extended dynamical tortoise coordinate transformation, Damour-Ruffini method has been applied to calculate the charged particles’ Hawking radiation from the apparent horizon of a dynamical Kerr-Newman black hole. It is shown that Hawking radiation is still purely thermal black body spectrum. Moreover, the temperature of Hawking radiation is corresponding to the apparent horizon surface gravity and the first law of thermodynamics can also be constructed successfully on the apparent horizon in the dynamical Kerr-Newman black hole.     

Quantum anomaly at horizon and Hawking radiation from higher dimensional Reissner–Nordström–de Sitter black hole

Based on the anomaly cancellation method, initiated by Robinson and Wilczek, we investigate Hawking radiation from the event horizon and cosmological horizon of the higher dimensional Reissner–Nordström–de Sitter black hole via covariant gauge and gravitational anomalies. Unlike in black hole space-time, to describe the observable physics, the effective field theory here is constructed between the event horizon and cosmological horizon. Our result shows that to restore the underlying gauge covariance and diffeomorphism covariance at the quantum level, the covariant compensating fluxes of gauge and energy–momentum tensor, which are shown to equal to those of Hawking radiation, should be radiated from the event horizon and absorbed from the cosmological horizon, respectively.     

Gibbons-Maeda dilaton黑洞的全息熵

依据全息原理,通过计算Gibbons-Maeda dilaton黑洞事件视界上量子场的统计熵,得到了该黑洞的全息熵和Bekenstein-Hawking熵.计算中利用非对易量子场论,克服了普通量子场论中态密度在视界上的发散困难,避免了黑洞熵热气体方法中紫外截断的引入.用留数定理克服了计算中的积分困难,所得的结果定量成立.研究表明,黑洞熵可以视为其视界上量子场的熵;通过计算视界上量子态的统计熵可以得到黑洞熵,计算中可以且应该避免视界外量子态的影响. 关键词： 黑洞熵 全息原理 事件视界 非对易量子场论     

Black Hole Entropies of the Thin Film Model and the Membrane Model Without Cutoffs

Taking into account the effect of the generalized uncertainty principle on the generalized black hole entropy and tacking the thin film brick-wall model, we calculate the entropy of the quantum scalar field in generalized static black hole. The Bekenstein–Hawking entropies of all well-known static black holes are obtained. The entropy of 2-D membrane just at the event horizon of static black hole is also calculated, and the result of the black hole entropy proportional to the event horizon area can be obtained more easily and generally. This discussion shows that black hole entropy is just identified with the entropy of the quantum field on the event horizon. The difference from the original brick-wall model is that the present result is convergent without any cutoff and the little mass approximation is removed. With residue theorem, the integral difficulty in the calculation of black hole entropy is overcome.     

Physical nature of the event horizon

It is shown by arguments based on the uncertainty principle that large fluctuations of the metric occur near the event horizon of a Schwarzschild black hole on a scale much larger than Planck length. The width of the transition layer about the event horizon and the associated surface tension are also estimated.     

The thermal radiation from dynamic black holes

Using the related formula of dynamic black holes, the instantaneous radiation energy density of the general spherically symmetric charged dynamic black hole and the arbitrarily accelerating charged dynamic black hole is calculated. It is found that the instantaneous radiation energy density of black hole is always proportional to the quartic of the temperature of event horizon in the same direction. The proportional coefficient of generalized Stefan-Boltzmann is no longer a constant, and it becomes a dynamic coefficient that is related to the event horizon changing rate, space-time structure near event horizon and the radiation absorption coefficient of the black hole. It is shown that there should be an internal relation between the gravitational field around black hole and its thermal radiation. Supported by the Science Foundation of Heze University (Grant No. XY06WL01)     

Horizon Entropy

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, extend quite generally to what we call here causal horizons. The root of this generalization is the local notion of horizon entropy density.     

从乌龟坐标在动态Vaidya黑洞上的推广谈起

从一类参数未定的一般形式的乌龟坐标变换出发, 找出了在动态Vaidya黑洞背景下能将波动方程化为标准形式且无发散的乌龟坐标所满足的条件. 结果表明, 以乌龟坐标变换为主要特征的Damour-Ruffini方法, 用来计算动态黑洞的Hawking辐射时, 只适用于事件视界, 无法应用于表观视界.     

一般球对称带电蒸发黑洞的温度

从视界附近的KleinGordon方程出发,准确地定出了一般球对称带电蒸发黑洞的Hawking温度和辐射谱,同时计算出事件视界方程.所得结果与用零曲面方程得到的结果一致 关键词： 蒸发黑洞 视界 辐射     

静态球对称黑洞热力学与爱因斯坦场方程

建立在广义相对论基础上的黑洞理论与热力学定律之间有着深刻的内在联系.具体考虑球对称黑洞,研究表明通过史瓦西黑洞和Reissner-Nordstrom黑洞在其视界附近的爱因斯坦场方程可以直接得到对应的黑洞热力学第一定律.这揭示了爱因斯坦引力场方程与黑洞热力学的关系,表明了在广义相对论理论框架下黑洞热力学规律的必然性.     

Nonequilibrium Thermodynamics of Dark Energy on Cosmic Apparent Horizon

In recent several years, some works have been done on cosmic thermodynamics.The apparent horizon was regarded as the key characteristic supersurface where thermodynamics can be built on perfectly. However, if the irreversible process is considered, the proper position for building thermodynamics will not be the apparent horizon anymore. The new position is related to dark energy state equation and the irreversible process parameters.     

The quantum nonthermal radiation and horizon surface gravity of an arbitrarily accelerating black hole with electric charge and magnetic charge

Using a new tortoise coordinate transformation,we discuss the quantum nonthermal radiation characteristics near an event horizon by studying the Hamilton-Jacobi equation of a scalar particle in curved space-time,and obtain the event horizon surface gravity and the Hawking temperature on that event horizon.The results show that there is a crossing of particle energy near the event horizon.We derive the maximum overlap of the positive and negative energy levels.It is also found that the Hawking temperature of a black hole depends not only on the time,but also on the angle.There is a problem of dimension in the usual tortoise coordinate,so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.     

Unitary dynamics of spherical null gravitating shells

The dynamics of a thin spherically symmetric shell of zero-rest-mass matter in its own gravitational field is studied. A form of action principle is used that enables the reformulation of the dynamics as motion on a fixed background manifold. A self-adjoint extension of the Hamiltonian is obtained via the group quantization method. Operators of position and of direction of motion are constructed. The shell is shown to avoid the singularity, to bounce and to re-expand to that asymptotic region from which it contracted; the dynamics is, therefore, truly unitary. If a wave packet is sufficiently narrow and/or energetic then an essential part of it can be concentrated under its Schwarzschild radius near the bounce point but no black hole forms. The quantum Schwarzschild horizon is a linear combination of a black and white hole apparent horizons rather than an event horizon.     

动态广义球对称含荷黑洞的量子熵

计算了广义球对称含荷黑洞视界上标量场的量子态数和自由能，得到了黑洞熵与视界面积成 正比的结论，表明黑洞熵就是其视界上的量子态的熵．考虑广义不确定原理对黑洞熵的影响 ，采用二维膜模型，克服了brick-wall模型中的发散困难，计算中无须任何截断，且brick- wall模型中的小质量近似也可以避免．对视界外二维膜上的量子场的熵做了级数展开讨论， 得到了一些值得探讨的结论． 关键词： 广义不确定原理 黑洞熵 视界 截断     

球对称动态黑洞视界附近的瞬时辐射能通量及瞬时辐射功率

采用黑洞的薄膜模型和局域热平衡的假定,研究球对称动态黑洞视界附近的瞬时辐射能通量和瞬时辐射功率,得到了当截断距离η取定后,Vaidya黑洞视界附近标量场的瞬时辐射能通量与黑洞的质量和视界变化率有关,其瞬时辐射功率仅与黑洞的视界变化率有关.Vaidya-Bonner黑洞的瞬时辐射能通量和瞬时辐射功率与黑洞的质量、电荷和视界变化率有关.表明黑洞周围的引力场、电磁场以及视界的变化均对黑洞的热辐射产生影响.     

Quantum nonthermal radiation and horizon surface gravity of an arbitrarily accelerating black hole with electric charge and magnetic charge

With a new tortoise coordinate transformation, we discussed the quantum nonthermal radiation characteristics near the event horizon by studying the Hamilton-Jacobi equation of a scalar particle in the curve space-time, and obtained the event horizon surface gravity and the Hawking temperature on the event horizon. The results showed that there is a crossing of particle energy near the event horizon. We derived the maximum overlap of the positive and negative energy levels. It was also found that the Hawking temperature of a black hole depends on not only the time, but also the angle. There is a problem of dimension in the usual tortoise coordinate, so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.     

Anomalies,Hawking Radiation in Taub-NUT Black Hole

In this paper, we mainly investigate the anomalous effective action of the rotating Taub-NUT black hole and show that the flux of Hawking radiation can be determined by anomaly cancellation conditions and regularity requirement at the event horizon. With the method of a dimensional reduction technique, that is, the (1+1) dimensional quantum anomalies equation, we successfully obtain the simplified metric near the horizon. In addition, the covariant energy-momentum tensor that is related with Hawking temperature are calculated in this black hole.