Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation

In this Letter we make a critique of, and comparison between, the anomaly method and WKB/tunneling method for obtaining radiation from non-trivial spacetime backgrounds. We focus on Rindler spacetime (the spacetime of an accelerating observer) and the associated Unruh radiation since this is the prototype of the phenomena of radiation from a spacetime, and it is the simplest model for making clear subtle points in the tunneling and anomaly methods. Our analysis leads to the following conclusions: (i) neither the consistent and covariant anomaly methods gives the correct Unruh temperature for Rindler spacetime and in some cases (e.g. de Sitter spacetime) the consistent and covariant methods disagree with one another; (ii) the tunneling method can be applied in all cases, but it has a previously unnoticed temporal contribution which must be accounted for in order to obtain the correct temperature.     

Tunnelling Effect and Hawking Radiation from a Vaidya Black Hole

We extend Parikh＇s study to the non-stationary black hole. As an example of the non-stationary black hole, we investigate the tunnelling effect and Hawking radiation from a Vaidya black hole whose Bondi mass is identical to its mass parameter. The Hawking radiation is considered as a tunnelling process across the event horizon and we calculate the tunnelling probability. It is found that the is the function of Bondi mass re（υ）. result is different from Parikh＇s study because dr H/dυ     

Charged particle's tunneling from a dilaton black hole

Hawking radiation viewed as a semi-classical tunneling process of charged particles from the event horizon of the Garfinkle–Horne dilaton black hole is investigated by taking into account not only energy conservation but also electric charge conservation. Our results show that when the effect of the emitted massive charged particle's self-gravitation is incorporated, the tunneling rate is related to the change of the black hole's Bekenstein–Hawking entropy and the emission spectrum deviates from the purely thermal spectrum.     

Tunnelling Effect of Two Horizons from a Gibbons--Maeda Black Hole

We study the thermal characters of the inner horizon of a Gibbons-Maeda black hole. In order to satisfy the Nernst theorem of the third law, the entropy of the black hole with two horizons must depend not only on the area of the outer horizon but also on the area of the inner horizon. Then the temperature of the inner horizon is calculated. Lastly, the tunnelling effect including the inner horizon of a Gibbons-Maeda black hole is investigated. We also calculate the tunnelling rate of the outer horizon Г＋ and the inner horizon Г_. The total tunnelling rate Г should be the product of the rates of the outer and inner horizon, Г =Г＋ · Г_. It is found that the total tunnelling rate is in agreement with the Parikh＇s standard result, Г→ exp（ ASBH ）, and there is no information loss.     

Brick Wall Model and the Spectrum of a Schwarzschild Black Hole

The quantum entropy of a scalar field near a Schwarzschild black hole is investigated by employing the brick-wall model in the grand canonical ensemble. A positive chemical potential is introduced if the cutoff is set to be of order of the Planck length. We also discuss the relation between the chemical potential and the mass quantum of the black hole.     

Tunnelling Effect of Massive Particles from Kerr Black Holes

In this paper, we extend Parikh’s (massless particles) and Zhang’ work to massive particles’ Kerr black hole tunnelling. By treating the massive particle as de Broglie wave, we calculate the emission rates of the particles across the event horizon of the Kerr black holes. Our result is successful and is in agreement with the form of the massless particles.     

Black hole entropy,log correction and inverse area correction

In this Letter, we first extend the Parikh–Wilczek tunneling framework to a general spherically symmetric black hole, and calculate the tunneling rate of the emission particles to the second order accuracy. Then, by assuming the emission process satisfies an underlying unitary theory, we correct the entropy of a general spherically symmetric black hole. We find that the log correction and the inverse area correction to the entropy is also suitable for a general spherically symmetric black hole.     

Hawking radiation of linear dilaton black holes

We compute exactly the semi-classical radiation spectrum for a class of non-asymptotically flat charged dilaton black holes, the so-called linear dilaton black holes. In the high frequency regime, the temperature for these black holes generically agrees with the surface gravity result. In the special case where the black hole is massless, we show that, although the surface gravity remains finite, there is no radiation, in agreement with the fact that massless objects cannot radiate.     

Black hole quantum tunnelling and black hole entropy correction

The Parikh–Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is investigated once more in this work. The first order correction, the log-corrected entropy-area relation, emerges naturally in the tunnelling picture if we consider the emission of a spherical shell. The second order correction to the emission rate for the Schwarzschild black hole is also calculated. At this level, the entropy of the black hole will contain three parts: the usual Bekenstein–Hawking entropy, a logarithmic term and an inverse area term. We find that the coefficient of the logarithmic term is −1. Thus, apart from a coefficient, our correction to the black hole entropy is consistent with that calculated in loop quantum gravity.     

Statistical-Mechanical Entropy of a Black Hole with a Global Monopole to All Orders in Planck Length

Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle, we calculate the statistical entropy of the scalar field in the global monopole black hole spacetime without any artificial cutoff. It is shown that the entropy is proportional to the horizon area.     

Dirac Particles＇ Hawking Radiation from a Schwarzschild Black Hole

Considering energy conservation and the backreaction of particles to spacetime, we investigate the massless/massive Dirac particles＇ Hawking radiation from a Schwarzschild black hole, The exact expression of the emission rate near the horizon is obtained and the result indicates that Hawking radiation spectrum is not purely thermal. The result obtained is consistent with the results obtained before. It satisfies the underlying unitary theory and offers a possible mechanism to explain the information loss paradox. Whereas the improved Damour-Rufflni method is more concise and understandable,     

Hawking temperature of Kerr–Newman–AdS black hole from tunneling

Using the null-geodesic tunneling method of Parikh and Wilczek, we derive the Hawking temperature of a general four-dimensional rotating black hole. In order to eliminate the motion of ? degree of freedom of a tunneling particle, we have chosen a reference system that is co-rotating with the black hole horizon. Then we give the explicit result for the Hawking temperature of the Kerr–Newman–AdS black hole from the tunneling approach.     

Hidden messenger revealed in Hawking radiation: A resolution to the paradox of black hole information loss

Using standard statistical method, we discover the existence of correlations among Hawking radiations (of tunneled particles) from a black hole. The information carried by such correlations is quantified by mutual information between sequential emissions. Through a careful counting of the entropy taken out by the emitted particles, we show that the black hole radiation as tunneling is an entropy conservation process. While information is leaked out through the radiation, the total entropy is conserved. Thus, we conclude the black hole evaporation process is unitary.     

Thermodynamics of warped AdS3 black hole in the brick wall method

The statistical entropy of a scalar field on the warped AdS₃ black hole in the cosmological topologically massive gravity is calculated based on the brick-wall method, which is different from the Wald's entropy formula giving the modified area law due to the higher-derivative corrections in that the entropy still satisfies the area law. It means that the entropy for scalar excitations on this background is independent of higher-order derivative terms or the conventional brick wall method has some limitations to take into account the higher-derivative terms.     

The temperature in Hawking radiation as tunneling

The quasi-classical method of deriving Hawking radiation under the consideration of canonical invariance is investigated. We find that the horizon should be regarded as a two-way barrier and the ingoing amplitude should be calculated according to the negative energy particles tunneling into the black hole because of the whole space–time interchange and thus the standard Hawking temperature is recovered. We also discuss the advantage of the Painlevé coordinates in Hawking radiation as tunneling.     

Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole

A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In the case of static metric of Banados-Teitelboim-Zanelli （BTZ） black hole, the field equations near the horizon boundary can be expressed as a thermal identity dE = TdS＋ Pr dA, where E = M is the mass of BTZ black hole, dA is the change in the area of the black hole horizon when the horizon is displaced infinitesimally small, Pr is the radial pressure provided by the source of Einstein equations, S = 41πa is the entropy and T =κ/2π is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole, showing that it is also possible to interpret the field equation near horizon as a thermodynamic identity dE = TdS ＋ PrdA ＋Ω＋dJ, where Ω＋ is the angular velocity and J is the angular momentum of BTZ black hole. These results indicate that the field equations for BTZ black hole possess intrinsic thermodynamic properties near the horizon.     

Gauss-Bonnet and Lovelock Gravities and the Generalized Second Law of Thermodynamics

It has been shown [Chin. Phys. Lett.25 （2008） 4199] that the generalized second law of thermodynamics holds in Einstein gravity. Here we extend this procedure for Gauss-Bonnet and Lovelock gravities. It is shown that by employing the general expression for temperature Th =｜κ｜/2π= 1/2πτA （1-τA/2HτA） associated with the apparent horizon of a Friedman Robertson-Walker （FRW） universe and assuming Tm = bTh, we are able to construct conditions for which the generalized second law holds in Gauss Bonnet and Lovelock gravities, where Tm and Th are the temperatures of the source and the horizon respectively.     

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.