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 thermodynamics and the factor of 2 problem

We show that the recent tunneling formulas for black hole radiation in static, spherically symmetric spacetimes follow as a consequence of the first law of black hole thermodynamics and the area-entropy relation based on the radiation temperature. A tunneling formula results even if the radiation temperature is different from the one originally derived by Hawking and this is discussed in the context of the recent factor of 2 problem. In particular, it is shown that if the radiation temperature is higher than the Hawking temperature by a factor of two, thermodynamics then leads to a tunneling formula which is exactly the one recently found to be canonically invariant.     

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.     

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 fermions tunnelling from Kerr–Newman black holes

We consider the tunnelling of charged spin 1/2 fermions from a Kerr–Newman black hole and demonstrate that the expected Hawking temperature is recovered. We discuss certain technical subtleties related to the obtention of this result.     

Can Hawking temperatures be negative?

It has been widely believed that the Hawking temperature for a black hole is uniquely determined by its metric and positive. But, I argue that this might not be true in the recently discovered black holes which include the exotic black holes and the black holes in the three-dimensional higher curvature gravities. I argue that the Hawking temperatures, which are measured by the quantum fields in thermal equilibrium with the black holes, might not be the usual Hawking temperature but the new temperatures that have been proposed recently and can be negative. The associated new entropy formulae, which are defined by the first and second laws of thermodynamics, versus the black hole masses show some genuine effects of the black holes which do not occur in the spin systems. Some cosmological implications and physical origin of the discrepancy with the standard analysis are noted also.     

Fermions tunnelling from GHS and non-extremal D1–D5 black holes

Recent research shows that fermions tunnelling can result in correct Hawking temperature of a black hole. In this letter, choosing a set of appropriate matrices γμ${\gamma }^{\mu }$, we attempt to study Hawking radiation of Dirac particles across the horizons of the GHS and non-extremal five-dimensional D1–D5 black holes in string theory by using fermions tunnelling method. Finally, the expected Hawking temperatures of the GHS and non-extremal D1–D5 black holes are correctly recovered.     

Casimir Energy in Hartle--Hawking State

We calculate the Casimir effect at finite temperature in Minkowski spacetime by using statistical method, the approximate expressions of the Casimir effect in the low and high temperature limits are also discussed. Then employing some general properties of the renormalized stress tensor, we obtain the Casimir energy stress tensor in Hattie-Hawking state.     

Statistical-Mechanical Entropies of Schwarzschild Black Hole due to Arbitrary Spin Fields in Different Coordinates

The statistical-mechanical entropies of the Schwarzschild black hole arising from the scalar, Weyl neutrino, electromagnetic, Rarita-Schwinger and gravitational fields are investigated in the Painlevg and Lemaitre coordinates. Although the metrics in the Painlevg and the Lemaitre coordinates do not obviously possess the singularity as that in the Schwarzschild coordinate, we find that the entropies of the arbitrary spin fields in both the Painlevd and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild coordinate.     

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.     

Anomalies and Hawking fluxes from the black holes of topologically massive gravity

The anomaly cancelation method proposed by Wilczek et al. is applied to the black holes of topologically massive gravity (TMG) and topologically massive gravito-electrodynamics (TMGE). Thus the Hawking temperature and fluxes of the ACL and ACGL black holes are found. The Hawking temperatures obtained agree with the surface gravity formula. Both black holes are rotating and this gives rise to appropriate terms in the effective U(1)$\mathrm{U}(1)$ gauge field of the reduced (1+1)$(1+1)$-dimensional theory. It is found that the terms in this U(1)$\mathrm{U}(1)$ gauge field correspond exactly to the correct angular velocities on the horizon of both black holes as well as the correct electrostatic potential of the ACGL black hole. So the results for the Hawking fluxes derived here from the anomaly cancelation method, are in complete agreement with the ones obtained from integrating the Planck distribution.     

Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces

Robinson–Wilczek's recent work shows that, the energy–momentum tensor flux required to cancel gravitational anomaly at the event horizon of a Schwarzschild-type black hole has an equivalent form to that of a (1+1)$(1+1)$-dimensional blackbody radiation at the Hawking temperature. Motivated by their work, Hawking radiation from the cosmological horizons of the general Schwarzschild–de Sitter and Kerr–de Sitter black holes, has been studied by the method of anomaly cancellation. The result shows that the absorbing gauge current and energy momentum tensor fluxes required to cancel gauge and gravitational anomalies at the cosmological horizon are precisely equal to those of Hawking radiation from it. It should be emphasized that the effective field theory for generic black holes in de Sitter spaces should be formulated within the region between the event horizon (EH) and the cosmological horizon (CH), to integrate out the classically irrelevant ingoing modes at the EH and the classically irrelevant outgoing modes at the CH, respectively.     

Massive Particle＇s Tunnelling from Black Hole with Topological Defect

We extend Zhang and Zhao＇s recent work to black hole with topological defect whose Arnowitt-Deser-Misner mass is no longer identical to its mass parameter. The behaviour of the tunnelling massive particles is investigated, and the emission rate at which massive particles tunnel across the event horizon of the black hole is calculated. The result is consistent with an underlying unitary theory, and takes the same functional form as that of mass-less particles.     

Extremal Kerr black hole/CFT correspondence in the five-dimensional Gödel universe

We extend the method of Kerr/CFT correspondence recently proposed in arXiv:0809.4266 [hep-th] to the extremal (charged) Kerr black hole embedded in the five-dimensional Gödel universe. With the aid of the central charges in the Virasoro algebra and the Frolov–Thorne temperatures, together with the use of the Cardy formula, we have obtained the microscopic entropies that precisely agree with the ones macroscopically calculated by Bekenstein–Hawking area law.     

Hawking radiation as tunneling and the unified first law of thermodynamics at the apparent horizon of the FRW universe

Relations between the tunneling rate FRW universe are investigated. The namics in such a dynamical system. first law of thermodynamics through and the unified first law of thermodynamics at the apparent horizon of the tunneling rate arises as a consequence of the unified first law of thermodyAnalysis shows how the tunneling is intimately connected with the unified the principle of conservation of energy.     

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.     

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.     

Fermions tunneling of higher-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter

The 1/2 spin fermions tunneling at the horizon of n-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter is researched via semi-classical approximation method, and the Hawking temperature and fermions tunneling rate are obtained in this Letter. Using a new method, the semi-classical Hamilton–Jacobi equation is gotten from the Dirac equation in this Letter, and the work makes several quantum tunneling theories more harmonious.     

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.