Parikh-Wilczek Tunneling as Massive Particles from Noncommutative Schwarzschild Black Hole

In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spacetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the hermodynamical relations in black hole. We calculate the emission rate of the massive particles' tunneling from aSchwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noncommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.     

Massive Particles' Tunneling Effect from An Arbitrarily Dimensional Schwarzschild Black Hole

According to Parikh's recent work, Hawking radiation is viewed as a tunneling process and the barrier is created just by the outgoing particle itself. In this paper, we extend Parikh's work to the case of massive particles' tunneling, and calculate the emission rate at which massive particles tunnel across the event horizon of an arbitrarily dimensional Schwarzschild black hole. The result is also consistent with an underlying unitary theory and takes the same functional form as that of massless particles. Moreover, our result also shows that Hawking radiation is an intrinstic property of the black hole.     

Hawking radiation and black hole entropy in a gravity’s rainbow

In the context of gravity’s rainbow, Planck scale correction on Hawking radiation and black hole entropy in Parikh and Wilczk’s tunneling framework is studied. We calculate the tunneling probability of massless particles in the modified Schwarzschild black holes from gravity’s rainbow. In the tunneling process, when a particle gets across the horizon, the metric fluctuation must be taken into account, not only due to energy conservation but also to spacetime Planck scale effect. Our results show that the emission rate is related to changes of the black hole’s quantum corrected entropies before and after the emission. In the same time, for the modified black holes, a series of correction terms including a logarithmic term to Bekenstein–Hawking entropy are obtained. Correspondingly, the spectrum of Planck scale corrected emission is obtained and it deviates from the thermal spectrum. In addition, a specific form of modified dispersion relation is proposed and applied.     

Black hole evaporation in a noncommutative charged Vaidya model

We study the black hole evaporation and Hawking radiation for a noncommutative charged Vaidya black hole. For this purpose, we determine a spherically symmetric charged Vaidya model and then formulate a noncommutative Reissner-Nordstr?m-like solution of this model, which leads to an exact (t ? r)-dependent metric. The behavior of the temporal component of this metric and the corresponding Hawking temperature are investigated. The results are shown in the form of graphs. Further, we examine the tunneling process of charged massive particles through the quantum horizon. We find that the tunneling amplitude is modified due to noncommutativity. Also, it turns out that the black hole evaporates completely in the limits of large time and horizon radius. The effect of charge is to reduce the temperature from a maximum value to zero. We note that the final stage of black hole evaporation is a naked singularity.     

静质量不为零的粒子的量子隧穿辐射

用量子隧穿法研究黑洞Hawking辐射，计算了静止质量不为零的粒子穿过Schwarzschild黑洞事件视界的出射率.所得结果满足幺正性原理，且与无质量粒子出射率具有相同的函数形式. 关键词： 黑洞 Hawking辐射 量子理论     

Research on Hawking Radiation as Tunneling from Schwarzshild-anti-de Sitter Black Hole

After taking into account energy conservation and the particle’s self-gravitation interaction, Hawking radiation of the massive particle as tunneling from Schwarzshild-anti-de Sitter black hole is studied by using Parikh-Wilczek’s semi-classical quantum tunneling approach. Meanwhile, Hawking radiation as tunneling from the black hole is reexamined by developing Angheben–Nadalini–Vanzo–Zerbini (ANVZ) covariant method to cover energy conservation and the particle’s self-gravitation interaction. Both the results perfectly generalize those obtained by Parikh and Wilczek, and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the factual emission spectrum is not exactly thermal, but satisfies the underlying unitary theory. PACS: 04.70-s, 9760. Lf.     

Quantum tunneling and trace anomaly

We compute the corrections, using the tunneling formalism based on a quantum WKB approach, to the Hawking temperature and Bekenstein–Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are shown to be equivalent to findings inferred from Hawking's original calculation based on path integrals using zeta function regularization. Finally, exploiting the corrected temperature and periodicity arguments we also find the modification to the original Schwarzschild metric which captures the effect of quantum corrections.     

Schwarzschild black hole in noncommutative spaces

We study the effects of noncommutative spaces on the horizon, the area spectrum and Hawking temperature of a Schwarzschild black hole. The results show deviations from the usual horizon, area spectrum and the Hawking temperature. The deviations depend on the parameter of space/space noncommutativity.     

Hawking radiation of Dirac particles from soft-hairy black holes

In this paper, we study the Hawking radiation of Dirac particles via tunneling formalism from linearly supertranslated Schwarzschild black holes. We find that the radiation spectrum and the Hawking temperature remain the same as the one without soft hair.     

Massive particle’s tunneling radiation from higher-dimensional Schwarzchild de Sitte and Anti-de Sitter black holes

We investigate the massive particle’s tunneling radiation from Schwarzchild black holes in higher-dimensional de Sitter and Anti-de Sitter space-times. Difference from the mass-less particle, the geodesics of the massive particle is not light-like, but decided by the phase velocity. We focus on s-waves, extend Parikh and Wilczek’s semi-classical tunneling method, and calculate the massive particle’s emission rate. It is shown that the emission rate is relevant to the change of the black hole’s entropy respectively, and the result takes the same functional form as that of the mass-less particle.     

Correction to Hawking Radiation Characteristics of Stationary Demianski-Newman Black Hole

The pure thermal spectrum in dragging coordinate system and the tunneling radiation characteristics across the event horizon for stationary Demianski-Newman black hole are researched. The result shows that the tunneling rate of the particle is relevant to Bekenstein-Hawking entropy, and the derived radiate spectrum is not strictly pure thermal, but is consistent with underlying unitary theory. Finally, we use the obtained results to reduce to stationary Kerr black hole and static Schwarzschild black hole, and find that only when ignoring the spectrum at higher energies is the tunneling radiation spectrum consistent with Hawking pure thermal one.     

Fermion tunneling from a non-static black hole with the internal global monopole

Kerner and Mann’s recent research shows that the Hawking temperature and tunneling rate can be obtained by the fermion tunneling method from the Rindler space-time and a general non-rotating black hole. In this paper, considering the tunneling particles with spin 1/2 and taking into account the particle’s self-gravitation in the dynamical background space-time, we further improve Kerner and Man’s fermion tunneling method to investigate Hawking radiation via tunneling from a non-static black hole with the internal global monopole. The result shows that the tunneling rate of the non-static black hole is related to the integral of the changing horizon besides the change of Bekenstein–Hawking entropy, which is different from the stationary cases. It also essentially implies that the unitary is violated for the reason that the black hole is non-stationary and cannot be treated as an isolated system.     

Quantum correction to the entropy of noncommutative BTZ black hole

In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative BTZ black hole is stable at some range of parameters.     

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

In the tunneling framework of Hawking radiation, charged particle’s tunneling in the modified Reissner-Nordstrom black hole from gravity’s rainbow is investigated. To this end, following the Schwarzschild solution in gravity’s rainbow, the metric of the modified Reissner-Nordstrom black hole is given. In the tunneling process, the metric fluctuation is taken into account, due to not only the energy conservation and electric charge conservation, but also the spacetime quantum effects. The calculation shows out that the emission rate satisfies the first law of black hole thermodynamics and is consistent with an underlying unitary theory. In addition, it is found that the entropy of the modified black hole is different to the Benkestein-Hawking entropy and the quantum corrections of the entropy appears.     

Hawking radiation and tunneling mechanism for a new class of black holes in Einstein–Gauss–Bonnet gravity

We study Hawking radiation in a new class of black hole solutions in 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 analyze Hawking radiation using the original method of quantization of a scalar field in the black hole background and with 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.     

Regular black hole in three dimensions

We find a new black hole in three-dimensional anti-de Sitter space by introducing an anisotropic perfect fluid inspired by the noncommutative black hole. This is a regular black hole with two horizons. We compare the thermodynamics of this black hole with that of a non-rotating BTZ black hole. The first-law of thermodynamics is not compatible with the Bekenstein–Hawking entropy.     

Is Hawking temperature modified by the quantum tunneling beyond semiclassical approximation

Hawking temperature of a static and spherically symmetric black hole beyond semiclassical approximation is studied. The calculations show us that different definition of the particle’s energy gives different Hawking temperature. However, we argue that the result obtained using the standard definition of the particle energy is reasonable because it keeps the validity of the first law of the thermodynamics, i.e., both the Hawking temperature and entropy are not modified by the quantum tunneling beyond semiclassical approximation. The result shows us that any hypothetical (^h/_2p){\hbar} corrections to the tunneling rate are to be interpreted not as quantum corrections to the Hawking temperature but as fluctuations about a thermal background.     

Entangled Particles Tunneling From a Schwarzschild Black Hole immersed in an Electromagnetic Universe with GUP

Quantum gravity has exciting peculiarities on the Planck scale.The effect of generalized uncertainty principle (GUP) to the entangled scalar/fermion particles’ tunneling from a Schwarzschild black hole immersed in an electromagnetic Universe is investigated by the help of semi-classical tunneling method. The quantum corrected Hawking temperature of this black hole with an external parameter “a” modifies the Hawking temperature for the entangled particles.     

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.     

Hawking Radiation of the Charged Particle Via Tunneling from the Reissner-Nordström Black Hole

Since Parikh and Wilczek proposed a semiclassical tunneling method to investigate the Hawking radiation of static and spherically symmetric black holes, the method has been extensively developed to study various black holes. However, in almost all of the subsequent papers, there exists a important shortcoming that the geodesic equation of the massive particle is defined inconsistently with that of the massless particle. In this paper, we propose a new idea to reinvestigate the tunneling radiation from the event horizon of the Reissner-Nordström black hole. In our treatment, by starting from the Lagrangian analysis on the action, we redefine the geodesic equation of the massive and massless particle via tunneling from the event horizon of the Reissner-Nordström black hole, which overcomes the shortcoming mentioned above. The highlight of our work is a new and important development for the Parikh-Wilczek’s semiclassical tunneling method.