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.     

Hawking Tunneling Radiation of a Particle with Electric and Magnetic Charge from Kerr-Newman-Kasuya Black Hole

Extending the Parikh＇s quantum tunneling method of an uncharged particle, we investigate the quantum radiation characteristics of a particle with electric and magnetic charge via tunneling from the event horizon of the Kerr-Newman Kasuya black hole. The derived result supports the Parikh＇s opinion and the correction to the thermal spectrum is of precisely the form that satisfies the underlying unitary quantum theory, and finally provides a might explanation to the black hole information puzzle.     

黑洞量子隧穿过程的时间

讨论了弯曲时空中黑洞量子隧穿的时间.在假定了黑洞量子隧穿是一个瞬时过程的情况下,通过利用WKB法得出了有静止质量粒子的量子隧穿辐射谱.该辐射谱表明对于在黑洞视界处有静止质量粒子的出射也满足量子力学中的幺正性原理,支持Parikh-Wilczek的结论.结果的合理性表明,在黑洞视界处的量子隧穿过程可以看成是一个瞬时过程.     

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     

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.     

Reissner-Nordstr?m de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型，研究了Reissner-Nordstrm de Sitter黑洞的量子隧穿效应.结果表明，在能量守恒的条件下，黑洞外视界和宇宙视界处的粒子出射率与Bekenstein-Hawking熵有关，辐射谱不再是严格的纯热谱.     

Radiation Characteristics of Stationary Axisymmetric Sen Black Hole as Tunneling

Taking energy conservation and angular momentum conservation into account, the tunneling radiation characteristics of stationary axisymmetric Sen black hole is studied in this paper with the quantum tunneling method and the results show that the tunneling rate of particle at the event horizon of the black hole is relevant to Bekenstein–Hawking entropy and that the radiation spectrum is not strictly pure thermal. PACS: 04.70_S, 97.60.Lf     

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.     

Corrected Hawking Tunneling Radiation in the Higher Dimensional Reissner-Nordström Black Hole

Based on the generalized uncertainty principle, in which the quantum gravitational effects are properly taken in to account, the corrected Bekenstein-Hawking entropy of the higher dimensional Reissner-Nordström black hole, up to the square order of Planck length, has been calculated. Using the corrected entropy, the black hole radiation probability has been calculated in the tunneling formalism, which is corrected up to the same order of the Planck length and a generalized quantum tunneling through the event horizon of the black hole is obtained.     

Fermion Tunneling from an Axis-Symmetric Black Hole beyond the Semiclassical Approximation

Based on the Hamilton-Jacobi method beyond the semiclassical approximation proposed by R. Baberjee and B.R. Majhi, Hawking radiation of Dirac particle as tunneling through the event horizon is calculated. It is shown that all quantum corrections in the fermion particle action are proportional to the usual semiclassical contribution. Under the conception of irreducible mass and the first law of thermodynamics, the modifications to Hawking temperature and Bekenstein-Hawking entropy are given for a Kerr-Newmann black hole.     

“Charged” particle’s tunneling from rotating black holes

The behavior of a scalar field theory near the event horizon in a rotating black hole background can be effectively described by a two dimensional field theory in a gauge field background. Based on this fact, we proposal that the quantum tunneling from rotating black hole can be treated as “charged” particle’s tunneling process in its effectively two dimensional metric. Using this viewpoint and considering the corresponding “gauge charge” conservation, we calculate the non-thermal tunneling rate of Kerr black hole and Myers–Perry black hole, and results are consistent with Parikh–Wilczek’s original result for spherically symmetric black holes. Especially for Myers–Perry black hole which has multi-rotation parameters, our calculation fills in the gap existing in the literature applying Parikh–Wilczek’s tunneling method to various types black holes. Our derivation further illuminates the essential role of effective gauge symmetry in Hawking radiation from rotating black holes.     

Quantum Gravity Effects on the Tunneling Radiation of the Einstein-Maxwell-Dilaton-Axion Black Hole

Taking into account effects of quantum gravity, we investigate the evaporation of an Einstein-Maxwell-Dilaton-Axion black hole. The corrected Hawking temperature is gotten respectively by the scalar particle’s and the fermion’s tunneling across the horizon. This temperature is lower than the original one derived by Hawking, which means quantum gravity effects slow down the rise of the temperature.     

Quantum gravity effects on spectroscopy of Kerr-Newman black hole in gravity’s rainbow

The effects of quantum gravity on spectroscopy for the charged rotating gravity’s rainbow are investigated in this paper. By utilizing an action invariant obtained from particles tunneling through the event horizon, the entropy and area spectrum for the modified Kerr-Newman black hole are derived. The equally spaced entropy spectrum characteristic of Bekenstein’s original derivation is recovered. And, the entropy spectrum is independent of the energy of the test particles, although the gravity’s rainbow itself is the energy dependent. Such that, the quantum gravity effects of gravity’s rainbow has no influence on the entropy spectrum. On the other hand, due to the spacetime quantum effects, the obtained area spectrum is different from the original Bekenstein spectrum. It is not equidistant and is dependent on the horizon area. And that, by analyzing the area spectrum from a specific rainbow function, a minimum area with a Planck scale is derived for the event horizon. At this point, the area quantum is zero and the black hole radiation stops. Thus, the black hole remnant for the gravity’s rainbow is obtained from the area quantization. In addition, the entropy for the modified Kerr-Newman black hole is calculated and the quantum correction to the area law is obtained and discussed.     

Quantum Tunneling Radiation of Kerr-NUT Black Hole

Based on particles in a dynamical geometry, extending the Parikh ＇s method of quantum tunneling, radiation, we deeply investigate the quantum tunneling radiation of Kerr-NUT bhck hole. When self-gravitating action, energy conservation, and angular momentum conservation are taken into account, the emission rate of the particle on the event horizon is related to the change of Bekenstein-Hawking entropy and the emission spectrum is not precisely thermal, but is consistent with an underlying unitary theory.     

On particle creation by black holes

Hawking's analysis of particle creation by black holes is extended by explicitly obtaining the expression for the quantum mechanical state vector ψ which results from particle creation starting from the vacuum during gravitational collapse. (Hawking calculated only the expected number of particles in each mode for this state.) We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. In agreement with previously known results, we find that we are led to a unique quantum scattering theory which is completely well behaved mathematically provided a certain condition is satisfied by the operators which describe the scattering of classical positive frequency solutions. In terms of these operators we derive the expression for the state vector describing particle creation from the vacuum, and we prove that S-matrix is unitary. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. There is some ambiguity in the theory in this case arising from freedom involved in defining what one means by “positive frequency” at the future event horizon. However, it is proven that the expression for the density matrix formed from ψ describing the emission of particles to infinity is independent of this choice, and thus unambiguous predictions for the results of all possible measurements at infinity are obtained. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail (i.e., not only in expected number of particles) with black body emission.     

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.     

de Sitter Tunneling,Emission Spectrum and Entropy/Area Quantum

The Banerjee-Majhi's recent work shows that the Hawking radiation and entropy/area quantum of the black hole horizon (EH) can be well described in the tunneling picture. In this paper, we develop this idea to the case o a de Sitter tunneling from the cosmological horizon (CH), and obtain the Hawking emission spectrum and entropy/area spectroscopy from the CH of the purely de Sitter black hole as well as the Schwarzschild-de Sitter black hole. It i interestingly found that the area of the CH is quantized by A = 4l 2 pl , as was given by Hod for the area quantum of -the EH by considering the Heisenberg uncertainty principle and Schwinger-type emission process. Also, we conclude from our derivation that the entropy/area quantum of the CH is universal in the sense that it is independent of the black hole parameters. This realization implies that, (at least) at a semiclassical level, the de Sitter gravity shares the similar quantum behavior as the usual gravity without presence of a cosmological constant.     

de Sitter Tunneling,Emission Spectrum and Entropy/Area Quantum

The Banerjee-Majhi's recent work shows that the Hawking radiation and entropy/area quantum of the black hole horizon (EH) can be well described in the tunneling picture. In this paper, we develop this idea to the case of a de Sitter tunneling from the cosmological horizon (CH), and obtain the Hawking emission spectrum and entropy/area spectroscopy from the CH of the purely de Sitter black hole as well as the Schwarzschild-de Sitter black hole. It is interestingly found that the area of the CH is quantized by Δ A=4l_pl², as was given by Hod for the area quantum of -the EH by considering the Heisenberg uncertainty principle and Schwinger-type emission process. Also, we conclude from our derivation that the entropy/area quantum of the CH is universal in the sense that it is independent of the black hole parameters. This realization implies that, (at least) at a semiclassical level, the de Sitter gravity shares the similar quantum behavior as the usual gravity without presence of a cosmological constant.     

带电带磁粒子的量子隧穿辐射

运用Parikh-Wilczek的半经典量子隧穿法,计算了带电带磁粒子穿过黑洞视界时的量子隧穿辐射谱.以带有时空拓扑缺陷的双荷Reissner-Nordstrǒm黑洞为例进行研究,计算结果表明带电带磁粒子的出射过程满足么正性原理,支持Parikh-Wilczek的结论,出射谱不再是纯热谱. 关键词： 黑洞 Hawking辐射 量子理论     

Quantum Tunneling Radiation of Reissner-Nordström de Sitter Black Hole with a Global Monopole

Applying Parikh's quantum tunneling model, we study the quantum tunneling radiation of Reissner-Nordström de Sitter black hole with a global monopole. The result shows that the tunneling rates at the event horizon and the cosmic horizon are related to Bekenstein-Hawking entropy if we take the energy conservation into consideration, and the true radiate spectrum is not precisely thermal.