“Tunnelling” Black-Hole Radiation with ϕ 3 Self-Interaction: One-Loop Computation for Rindler Killing Horizons

Tunnelling processes through black hole horizons have recently been investigated in the framework of WKB theory discovering interesting interplay with the Hawking radiation. A more precise and general account of that phenomenon has been subsequently given within the framework of QFT in curved spacetime by two of the authors of the present paper. In particular, it has been shown that, in the limit of sharp localization on opposite sides of a Killing horizon, the quantum correlation functions of a scalar field appear to have thermal nature, and the tunnelling probability is proportional to exp{?β _Hawking E}. This local result is valid in every spacetime including a local Killing horizon, no field equation is necessary, while a suitable choice for the quantum state is relevant. Indeed, the two-point function has to verify a short-distance condition weaker than the Hadamard one. In this paper we consider a massive scalar quantum field with a ? ³ self-interaction and we investigate the issue whether or not the black hole radiation can be handled at perturbative level, including the renormalisation contributions. We prove that, for the simplest model of the Killing horizon generated by the boost in Minkowski spacetime, and referring to Minkowski vacuum, the tunnelling probability in the limit of sharp localization on opposite sides of the horizon preserves the thermal form proportional to exp{?β _H E} even taking the one-loop renormalisation corrections into account. A similar result is expected to hold for the Unruh state in the Kruskal manifold, since that state is Hadamard and looks like Minkowski vacuum close to the horizon.     

Discussion on the event horizon and quantum ergosphere of dynamic rotating black holes in a tunneling framework

According to the Parikh--Wilczek tunneling framework, the locations of the local horizons of dynamic rotating black holes can be worked out. The calculations show that the quantum ergosphere of the black hole is identical with the tunneling potential barrier set by particle's tunneling across the relevant horizon. Then, some discussions on the origin of the Hawking radiation will be shown.     

Discussion on event horizon and quantum ergosphere of dynamic rotating black holes in a tunneling framework

According to the Parikh-Wilczek tunneling framework, the locations of the local horizons of dynamic rotating black holes can be worked out. The calculations show that the quantum ergosphere of the black hole is identical with the tunneling potential barrier set by particle’s tunneling across the relevant horizon. Then, some discussions on the origin of the Hawking radiation will be shown.     

Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

A stationary solution of the Dirac equation in the metric of a Reissner-Nordström black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is physically self-consistent. The existence of quantum levels below the Cauchy horizon can affect the final stage of Hawking black hole evaporation and opens up the fundamental possibility of investigating the internal structure of black holes using quantum tunneling between external and internal states.     

Holographic Entropy Bound of a Nonstationary Black Hole

In accordance with the holographic principle, by counting the states of the scalar field just at the event horizon of the Vaidya-Bonner black hole, the holographic entropy bound of the black hole is calculated and the Bekenstein- Hawking formula is obtained, With the generalized uncertainty principle, the divergence of state density at event horizon in the ordinary quantum field theory is removed, With the residue theorem, the integral trouble in the calculation is overcome. The present result is quantitatively tenable and the holographic principle is realized by applying the quantum field theory to the black hole entropy problem. Compared with some previous works, it is suggested that the quantum states contributing to black hole entropy should be restricted on the event horizon.     

Hawking Radiation of Apparent Horizon in a FRW Universe as Tunneling Beyond Semiclassical Approximation

An analysis of Hawking radiation about apparent horizon in a FRW universe is performed by using the method developed in the paper (Banerjee, Majhi in JHEP 06:095 2008), in which the Hawking radiation of a black hole is treated as the quantum tunneling by Hamilton-Jacobi method beyond semiclassical approximation and then all the higher order quantum corrections can be given out. In our analysis, the Kodama vector instead of the Killing vector to define the energy of the particle plays a key role. We present our analysis under the Friedmann-Robertson-Walker like coordinate system and the much-like to Painlevé coordinate system respectively. The result show that the formulized procedure can be extended to fully analyse the Hawking radiation of a dynamical system.     

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     

缓变动态Kerr-Newman黑洞的量子热力学性质

引入局域热平衡概念，用Damour-Ruffini方法和薄膜模型研究了缓变动态Kerr-Newman黑洞的Hawking辐射和熵.得到了黑洞的Hawking温度和辐射谱公式，Hawking温度随时间和视界面上的位置而变化，辐射谱为准黑体谱；计算了黑洞熵，当取与静态球对称黑洞情况相同的截断关系时便得到了黑洞的Bekenstein-Hawking熵.结果表明，缓变动态黑洞的温度是局域量，缓变动态黑洞的熵与稳态黑洞情况一样正比于黑洞视界面面积. 关键词： 缓变动态黑洞 Hawking辐射 黑洞熵     

Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox

We revisit in detail the paradox of black hole information loss due to Hawking radiation as tunneling. We compute the amount of information encoded in correlations among Hawking radiations for a variety of black holes, including the Schwarzchild black hole, the Reissner–Nordström black hole, the Kerr black hole, and the Kerr–Newman black hole. The special case of tunneling through a quantum horizon is also considered. Within a phenomenological treatment based on the accepted emission probability spectrum from a black hole, we find that information is leaked out hidden in the correlations of Hawking radiation. The recovery of this previously unaccounted for information helps to conserve the total entropy of a system composed of a black hole plus its radiations. We thus conclude, irrespective of the microscopic picture for black hole collapsing, the associated radiation process: Hawking radiation as tunneling, is consistent with unitarity as required by quantum mechanics.     

探讨黑洞Hawking辐射的新方法——量子统计法

将黑洞看作由裸黑洞和二维热力学面(黑洞的视界)组成的正则系综,利用量子统计方法给出黑洞Hawking 辐射的能量谱.找到黑洞辐射温度与熵的关系. 关键词： Hawking辐射 正则系统 量子统计     

Stochastic equations in black hole backgrounds and non-equilibrium fluctuation theorems

We apply the non-equilibrium fluctuation theorems developed in the statistical physics to the thermodynamics of black hole horizons. In particular, we consider a scalar field in a black hole background. The system of the scalar field behaves stochastically due to the absorption of energy into the black hole and emission of the Hawking radiation from the black hole horizon. We derive the stochastic equations, i.e. Langevin and Fokker-Planck equations for a scalar field in a black hole background in the ?→0 limit with the Hawking temperature ?κ/2π fixed. We consider two cases, one confined in a box with a black hole at the center and the other in contact with a heat bath with temperature different from the Hawking temperature. In the first case, the system eventually becomes equilibrium with the Hawking temperature while in the second case there is an energy flow between the black hole and the heat bath. Applying the fluctuation theorems to these cases, we derive the generalized second law of black hole thermodynamics. In the present paper, we treat the black hole as a constant background geometry.Since the paper is also aimed to connect two different areas of physics, non-equilibrium physics and black holes physics, we include pedagogical reviews on the stochastic approaches to the non-equilibrium fluctuation theorems and some basics of black holes physics.     

Quantum Thermal Effect of Nonstationary Kerr-Newman Black Hole

The Hawking radiation and the entropy of non-stationary Kerr-Newman black hole whose metric changes slowly are calculated via the method of Damour etc. and the thin film brick-wall model. First, we obtain the Hawking radiation temperature and the thermal spectrum formula. Second, we get the entropy density at every point of the horizon surface as well as the total entropy of the black hole, which is just the Bekenstein-Hawking entropy and relies on the notion of the local equilibrium crucially that can be met if the evaporation and the accretion of the black hole is negligible. The results show that the temperature of the event horizon depends on the time and the angle, and the entropy of the non-stationary black hole is also proportional to the horizon area with appropriate cutoff relationship as in the case of stationary black holes.     

Charged Particles’ Hawking Radiation via Tunneling of Both Horizons from Reissner-Nordström-Taub-NUT Black Holes

In some recent derivations thermal characters of the inner horizon have been employed; however, the understanding of possible role that may play the inner horizons of black holes in black hole thermodynamics is still somewhat incomplete. Motivated by this problem we investigate Hawking radiation of the Reissner-Nordström-Taub-NUT (RNTN) black hole by considering thermal characters of both the outer and inner horizons. We apply Damour-Ruffini method and the thin film brick wall model to calculate the temperature and the entropy of the inner horizon of the RNTN black hole. The inner horizon admits thermal character with positive temperature and entropy proportional to its area, and it thus may contribute to the total entropy of the black hole in the context of Nernst theorem. Considering conservations of energy and charge and the back-reaction of emitting particles to the spacetime, the emission spectra are obtained for both the inner and outer horizons. The total emission rate is the product of the emission rates of the inner and outer horizons, and it deviates from the purely thermal spectrum and can bring some information out. Thus, the result can be treated as an explanation to the information loss paradox.     

Hawking Radiation of Black Hole in Einstein-Proca Theory

The Hawking radiation of black hole in Einstein-Proca theory is discussed in this paper. The Einstein-Proca black hole is more general than Reissner-Nordström black hole, because Proca field is massive vector field. We calculate several quantum perturbations in this spacetime, and obtain the Hawking radiation at the horizon in Einstein-Proca theory.     

Vaidya-Bonner-de Sitter时空中荷电Dirac粒子的Hawking辐射

在Vaidya-Bonner-de Siter时空中，准确地给出了黑洞内外视界及宇宙视界的位置，研究了该时空中黑洞外视界和宇宙视界附近荷电Dirac粒子的Hawking辐射，确定三个视界面中任何两个都不可能重合． 关键词：     

Instabilities in an Optical Black‐Hole Laser

The Hamiltonian of optical fields in a nonlinear dispersive fiber is studied. Quantum field fluctuations are spontaneously created close to an optical event horizon through the analog Hawking effect. The simplest model is considered for an optical black‐hole laser, where the Hawking radiation is produced and amplified inside a cavity formed by two horizons: a black hole and a white hole. It is found that resonant Hawking radiation originates from a discrete set of instabilities and tunnels out of the horizons. Finally, the numerical results are compared with the resonance and instability conditions and a phenomenological model is developed to give a clear physical picture.     

Tunneling Radiation of Massive Vector Bosons from Dilaton Black Holes

It is well known that Hawking radiation can be treated as a quantum tunneling process of particles from the event horizon of black hole. In this paper, we attempt to apply the massive vector bosons tunneling method to study the Hawking radiation from the non-rotating and rotating dilaton black holes. Starting with the Proca field equation that govern the dynamics of massive vector bosons, we derive the tunneling probabilities and radiation spectrums of the emitted vector bosons from the static spherical symmetric dilatonic black hole, the rotating Kaluza-Klein black hole, and the rotating Kerr-Sen black hole. Comparing the results with the blackbody spectrum, we satisfactorily reproduce the Hawking temperatures of these dilaton black holes, which are consistent with the previous results in the literature.     

Quantum black hole and Hawking radiation in a microscope of thermodynamical approach

We establish the state in which Hawking radiation is stopped by a quantum Schwarzschild black hole in the framework of quasi-classical thermal quantization for particles behind the horizon. The mechanism of absorption and radiation by the black hole is presented.     

Has Hawking Radiation Been Measured?

It is argued that Hawking radiation has indeed been measured and shown to posses a thermal spectrum, as predicted. This contention is based on three separate legs. The first is that the essential physics of the Hawking process for black holes can be modelled in other physical systems. The second is the white hole horizons are the time inverse of black hole horizons, and thus the physics of both is the same. The third is that the quantum emission, which is the Hawking process, is completely determined by measurements of the classical parameters of a linear physical system. The experiment conducted in 2010 fulfils all of these requirements, and is thus a true measurement of Hawking radiation.