Abstract:
Hawking radiation from the black hole in Horava-Lifshitz gravity is discussed by a reformulation of the tunneling method given in \cite{Banerjee:2008sn}. Using a density matrix technique the radiation spectrum is derived which is identical to that of a perfect black body. The temperature obtained here is proportional to the surface gravity of the black hole as occurs in usual Einstein gravity. The entropy is also derived by using the first law of black hole thermodynamics. Finally, the spectrum of entropy/area is obtained. The latter result is also discussed from the viewpoint of quasi-normal modes. Both methods lead to an equispaced entropy spectrum, although the value of the spacing is not the same. On the other hand, since the entropy is not proportional to the horizon area of the black hole, the area spectrum is not equidistant, a finding which also holds for the Einstein-Gauss-Bonnet theory.

Abstract:
A modern and largely used approach to obtain Hawking radiation is the tunnelling mechanism. However, in various papers in the literature, the analysis concerned almost only to obtain the Hawking temperature through a comparison of the probability of emission of an outgoing particle with the Boltzmann factor. In a interesting and well written paper, Banerjee and Majhi improved the approach, by explicitly finding a black body spectrum associated with black holes. On the other hand, this result, which has been obtained by using a reformulation of the tunnelling mechanism, is in contrast which the remarkable result by Parikh and Wilczek, that, indeed, found a probability of emission which is compatible with a non-strictly thermal spectrum. By using our recent introduction of an effective state for a black hole, here we solve such a contradiction, through a slight modification of the analysis by Banerjee and Majhi. The final result will be a non-strictly black body spectrum from the tunnelling mechanism. We also show that, for an effective temperature, we can write the corresponding effective metric by Hawking's periodicity arguments. Potential important implications for the black hole information puzzle are also discussed

Abstract:
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-Nordstr\"{o}m 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.

Abstract:
Planck scale corrections arising from deformed special relativity on Hawking radiation in Parikh and Wilczk's tunneling framework are studied. We calculate the emission rate of massless particles tunneling though the corrected horizon of modified black holes from gravity's rainbow. In the tunneling process, when a particle get across the quantum horizon, the metric fluctuation not only due to the energy conservation but also quantum effects of the space-time are taken into account. Our results show that, the emission rate is related to the changes of the black hole's quantum corrected entropy and consistent with an underlying unitary theory. In the modified black hole, by using black hole thermodynamics, a series of quantum correction terms including a logarithmic term to the Bekenstein-Hawking entropy are obtained. Correspondingly, the Planck scale corrected emission spectrum is obtained and it deviates from the thermal spectrum.

Abstract:
We study the Hawking radiation in a new class of black hole solutions in the Einstein-Gauss-Bonnet theory. The black hole has been argued to have vanishing mass and entropy, but finite Hawking temperature. To check if it really emits radiation, we analyse the Hawking radiation using the original method of quantization of scalar field in the black hole background and the quantum tunneling method, and confirm that it emits radiation at the Hawking temperature. A general formula is derived for the Hawking temperature and backreaction in the tunneling approach. Physical implications of these results are discussed.

Abstract:
Recent work, which treats the Hawking radiation as a semi-classical tunneling process at the horizon of the Schwarzschild and Reissner-Nordstrom spacetimes, indicates that the exact radiant spectrum is no longer pure thermal after considering the black hole background as dynamical and the conservation of energy. In this paper, we extend the method to investigate Hawking radiation as massless particles tunneling across the event horizon of the Kerr black hole and that of charged particles from the Kerr-Newman black hole by taking into account the energy conservation, the angular momentum conservation, and the electric charge conservation. Our results show that when self-gravitation is considered, the tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum, but is consistent with an underlying unitary theory.

Abstract:
Applying Parikh's semi-classical tunneling method, we consider Hawking radiation of the charged massive particles as a tunneling process from the Reissner-Nordstrom-de Sitter black hole with a global monopole. The result shows that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the radiant spectrum is not a pure thermal one, but is consistent with an underlying unitary theory.

Abstract:
Acoustic waves in fluids undergoing the transition from sub- to supersonic flow satisfy governing equations similar to those for light waves in the immediate vicinity of a black hole event horizon. This acoustic analogy has been used by Unruh and others as a conceptual model for `Hawking radiation.' Here we use variational methods, originally introduced by Brizard for the study of linearized MHD, and ray phase space methods, to analyze linearized acoustics in the presence of background flows. The variational formulation endows the evolution equations with natural Hermitian and symplectic structures that prove useful for later analysis. We derive a $2\times 2$ normal form governing the wave evolution in the vicinity of the `event horizon.' This shows that the acoustic model can be reduced locally (in ray phase space) to a standard (scalar) tunneling process weakly coupled to a unidirectional non-dispersive wave (the `incoming wave'). Given the normal form, the Hawking `thermal spectrum' can be derived by invoking standard tunneling theory, but only by ignoring the coupling to the incoming wave. Deriving the normal form requires a novel extension of the modular ray-based theory used previously to study tunneling and mode conversion in plasmas. We also discuss how ray phase space methods can be used to change representation, which brings the problem into a form where the wave functions are less singular than in the usual formulation, a fact that might prove useful in numerical studies.

Abstract:
We examine Hawking radiation from a Schwarzschild black hole in several reference frames using the quasi-classical tunneling picture. It is shown that when one uses, $\Gamma \propto \exp(Im [\oint p dr])$, rather than, $\Gamma \propto \exp(2 Im [\int p dr])$, for the tunneling probability/decay rate one obtains twice the original Hawking temperature. The former expression for $\Gamma$ is argued to be correct since $\oint p dr$ is invariant under canonical transformations, while $\int p dr$ is not. Thus, either the tunneling methods of calculating Hawking radiation are suspect or the Hawking temperature is twice that originally calculated.

Abstract:
This paper presents a straightforward derivation of Hawking radiation from a static black hole possessing mass-quadrupole moment as a tunneling process,and the radiation spectrum is obtained.Because the derivation assumes conservation laws,the exact spectrum is not precisely thermal. This result supports the viewpoint that it is possible for the radiation via tunneling to have information-carrying capabilities.