Spectroscopy of a Kerr–Newman–Kasuya Black Hole

Majhi and Vagenas’s work showed that the entropy spectrum of a spherically symmetric black hole can be obtained without quasinormal modes. In this paper, we extend this work to a Kerr–Newman–Kasuya black hole and discuss its spectra of entropy and area. We find that the spectra are equally spaced and are independent on the parameters of black hole.     

引力彩虹时空中Kerr黑洞的熵谱和面积谱

利用黑洞的绝热不变性,研究了引力彩虹时空中Kerr黑洞的熵谱和面积谱.首先,在引力彩虹时空背景下,计算了Kerr黑洞的绝热不变作用量,并将其与玻尔-索末菲量子化条件相结合,给出了黑洞的熵谱.得到的熵谱没有引力彩虹时空本身具有的粒子能量依赖性,且是与经典Kerr黑洞中原始贝肯斯坦熵谱相同的等间距熵谱.然后,根据黑洞热力学第一定律和黑洞熵谱,给出了与原始贝肯斯坦谱不同的面积谱.该面积谱是非等间距的,而且有对黑洞面积的依赖性,但不依赖于探测粒子的能量.面积谱表明,随着黑洞面积的减少,面积间隔逐步变小;当黑洞达到普朗克尺度时,面积量子可降为零.这表示黑洞面积不再减少,黑洞出现辐射剩余.而在忽略色散关系的修正效应或在大黑洞极限下,面积谱的修正项可以忽略,引力彩虹Kerr黑洞面积谱可以回归到原始贝肯斯坦谱.此外,对引力彩虹时空Kerr黑洞的熵进行了讨论,得到了带有面积倒数修正项的黑洞熵,分析了黑洞熵的量子修正与面积谱量子修正的一致性.     

Area Entropy and Quantized Mass of Black Holes from Information Theory

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy.     

f(T) cosmology via Noether symmetry

Using the modified Kunstatter method, which employs as proper frequency the imaginary part instead of the real part of the quasinormal modes, the entropy spectrum and area spectrum of the modified Schwarzschild black holes in gravity??s rainbow are investigated. In the current study, two cases of modified dispersion relations concerning energy dependent and energy independent speed of light are considered. The entropy spectra with equal spacing are derived in these two cases. Furthermore, the obtained entropy spectra are independent of the energy of a test particle and are the same as the one of the usual Schwarzschild black hole. Also, the same area spectrum formulas are obtained in these different dispersion relations. However, due to the quantum effect of spacetime, the obtained area spectra are not equally spaced and are different from the one of the usual Schwarzschild black hole. Besides, in these two cases, the same black hole entropy formulas with logarithmic correction to the standard Bekenstein?CHawking area formula are obtained by the adiabatic invariant. The form of area spacing formulas and entropy formulas are independent of the particle??s energy, but the area spacing and entropy can have energy dependence through the area.     

Spectroscopy of the Reissner–Nordström–Anti-de Sitter Black Hole via Adiabatic Invariance

By combining the black hole property of adiabaticity and the oscillating velocity of the black hole horizon, we study the entropy and the area spectra of the Reissner–Nordström–anti-de Sitter black hole. Instead of using the quasi-normal mode frequencies, we utilize the oscillating velocity of the event horizon in the tunneling framework to obtain the black hole spectroscopy via adiabatic invariance. The results show that, both of the area spectrum and the entropy spectrum are equally spaced and independent on the parameters of the black hole.     

Spectroscopy of the Einstein–Maxwell–Dilaton–Axion black hole

The entropy spectrum of a spherically symmetric black hole was derived via the Bohr–Sommerfeld quantization rule in Majhi and Vagenas’s work. Extending this work to charged and rotating black holes, we quantize the horizon area and the entropy of an Einstein–Maxwell–Dilaton–Axion black hole via the Bohr–Sommerfeld quantization rule and the adiabatic invariance. The result shows the area spectrum and the entropy spectrum are respectively equally spaced and independent on the parameters of the black hole.     

Area Spectrum of D-Dimensional Large Schwarzschild-AdS Black Hole from Asymptotic Quasinormal Modes

We investigate the area and entropy spectra of D-dimensional large Schwarzschild black holes. By utilizing the new physical interpretation of quasinormal mode frequency we find that a large Schwarzschild-AdS black hole has an equally spaced area spectrum and an equidistant entropy spectrum; both are dependent on the spacetime dimension.     

The Quantum Formulation of Black Hole Area Spectrum and Entropy Spectrum

In this paper, the area spectrum of this static BTZ black hole in different cases (rotating, non-rotating, and extreme) is investigated. The final results show that the spectral formulation is 2πnℏ when this black hole is non-rotating. For the black hole in other two different cases, its spectrum is angular momentum-dependent. Unexpectedly, their area spectra are both equally spaced. What is more, the entropy spectrum is also calculated via the method put forward by Chen et al. However, it is demonstrated that the well known area-entropy law is greatly changed. Above all, the entropy spectrum of this non-rotating BTZ black hole is also equally spaced.     

Calculating Entropy of Plane Symmetry Black Hole via Generalized Uncertainty Relation

The generalized uncertainty relation is introduced to calculate entropy of the black hole. By using quantum statistical method, we directly obtain the partition function of Bose and Fermi field on the background of the plane symmetry black hole. Then we calculate the entropy of Bose and Fermi field on the background of black hole near the horizon of the black hole. In our calculation, we need not introduce cutoff. There are not the left out term and the divergent logarithmic term in the original brick-wall method. And it is obtained that the entropy of the black hole is proportional to the area of the horizon. The inherent contact between the entropy of black hole and the area of horizon is opened out. Further it is shown the entropy of black hole is entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect.     

Hawking Radiation from Charged Kerr Black Hole Beyond Semi-classical Approximation

The Hawking radiation from charged Kerr black hole via the method beyond semi-classical approximation is studied. In our work, we apply the WKB approximation method and the quantum tunneling method, then calculate the tunneling rate and further correct Hawking entropy to charged Kerr black hole. It is shown that the result is still in agreement with the unitary theory, the entropy of the black hole contains three parts: the usual Bekenstein-Hawking entropy, the logarithmic term and the inverse area term. Apart from coefficients, our correction to the charged Kerr black hole entropy is consistent with results of loop quantum gravity.     

The Schwarzschild black hole’s remnant via the Bohr-Sommerfeld quantization rule

A d-dimensional Schwarzschild black hole is quantized by the action variable and the Bohr-Sommerfeld quantization rule in this paper. We find that the spectra of the horizon area and the entropy are evenly spaced. The black hole mass is also quantized and it’s spectrum spacing is proportional inversely to the mass. The ground state appears and has a constant entropy $\pi k_B$ . The ground state mass is shown to be the black hole remnant predicted by the generalized uncertainty principle and may be a candidate of dark matter.     

Sen黑洞熵与能斯特定理

避开求解黑洞背景下波动方程的困难,应用量子统计方法,直接求解轴对称Sen黑洞背景下Bose场和Fermi场的配分函数.然后利用改进的 brick-wall 方法-膜模型,计算黑洞背景下Bose场和Fermi场的熵.得到黑洞熵不但与黑洞的外视界面积有关，而且也是内视界面积的函数.在所得结论中不存在对数发散项与舍去项,也不存在黑洞视界外标量场或Dirac场为什么是黑洞熵疑难,并且给出粒子的自旋简并度对黑洞熵的影响. 当黑洞的辐射温度趋于绝对零度时,由黑洞内外视界面积决定的黑洞熵也趋于零,它满足能斯特定理,可视 关键词： 膜模型 黑洞熵 能斯特定理     

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.     

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.     

Area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes from quasinormal modes

The area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes are investigated from quasinormal modes via Maggiore’s physical interpretation of quasinormal modes. Using the first law of black hole thermodynamics and the action variable quantization, we arrive at consistent equally spaced area and entropy spectra. Results show that the spectra are irrelevant to the parameters of the black holes and the perturbation fields, which fully agree with Bekensteins original conjecture. In the calculations, we have defined the corresponding Hawking temperatures of the black holes following the suggestion of Mäkelä et al. to avoid the zero temperature and to guarantee the (nearly-) extreme black holes quantizable.     

Black Hole Entropies of the Thin Film Model and the Membrane Model Without Cutoffs

Taking into account the effect of the generalized uncertainty principle on the generalized black hole entropy and tacking the thin film brick-wall model, we calculate the entropy of the quantum scalar field in generalized static black hole. The Bekenstein–Hawking entropies of all well-known static black holes are obtained. The entropy of 2-D membrane just at the event horizon of static black hole is also calculated, and the result of the black hole entropy proportional to the event horizon area can be obtained more easily and generally. This discussion shows that black hole entropy is just identified with the entropy of the quantum field on the event horizon. The difference from the original brick-wall model is that the present result is convergent without any cutoff and the little mass approximation is removed. With residue theorem, the integral difficulty in the calculation of black hole entropy is overcome.     

Charged Particles’ Hawking Radiation via Tunneling of Both Horizons from Reissner-Nordström-Taub-NUT Black Holes

In some recent derivations thermal characters of the inner horizon have been employed; however, the understanding of possible role that may play the inner horizons of black holes in black hole thermodynamics is still somewhat incomplete. Motivated by this problem we investigate Hawking radiation of the Reissner-Nordström-Taub-NUT (RNTN) black hole by considering thermal characters of both the outer and inner horizons. We apply Damour-Ruffini method and the thin film brick wall model to calculate the temperature and the entropy of the inner horizon of the RNTN black hole. The inner horizon admits thermal character with positive temperature and entropy proportional to its area, and it thus may contribute to the total entropy of the black hole in the context of Nernst theorem. Considering conservations of energy and charge and the back-reaction of emitting particles to the spacetime, the emission spectra are obtained for both the inner and outer horizons. The total emission rate is the product of the emission rates of the inner and outer horizons, and it deviates from the purely thermal spectrum and can bring some information out. Thus, the result can be treated as an explanation to the information loss paradox.     

Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole

In this paper, by using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the 5-dimensional rotating black hole. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. And it is obtained that the entropy of the black hole is not only related to the area of the outer horizon but also is the function of inner horizon‘s area. In our results, there are not the left out term and the divergent logarithmic term in the original brick-wall method.The doubt that why the entropy of the scalar or Dirac field outside the event horizon is the entropy of the black hole in the original brick-wall method does not exist. The influence of spinning degeneracy of particles on entropy of the black hole is also given. It is shown that the entropy determined by the areas of the inner and outer horizons will approach zero,when the radiation temperature of the black hole approaches absolute zero. It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy. We provide a way to study higher dimensional black hole.     

Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole

In this paper, by using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the 5-dimensional rotating black hole. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. And it is obtained that the entropy of the black hole is not only related to the area of the outer horizon but also is the function of inner horizon‘s area. In our results, there are not the left out term and the divergent logarithmic term in the original brick-wall method.The doubt that why the entropy of the scalar or Dirac field outside the event horizon is the entropy of the black hole in the original brick-wall method does not exist. The influence of spinning degeneracy of particles on entropy of the black hole is also given. It is shown that the entropy determined by the areas of the inner and outer horizons will approach zero,when the radiation temperature of the black hole approaches absolute zero. It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy. We provide a way to study higher dimensional black hole.     

Entropy correction to stationary black hole via fermions tunneling beyond semiclassical approximation

Recently, fermions tunneling beyond semiclassical approximation from an uncharged static black hole was investigated by Majhi, which was based on the work of Banerjee and Majhi, it was found that the black hole entropy correction can be produced as the quantum effect of a particle is taken into account. In this paper, we further extend this idea to the stationary Kerr black hole to discuss its entropy correction. To get the corrections correctly, the proportionality parameters of quantum corrections of action I _i to the semiclassical action I ₀ in this case are regarded as the inverse of the product of Planck Length and Planck Mass. The result shows that entropy corrections to the stationary black hole also include the logarithmic term and inverse area term in Bekenstein–Hawking entropy beyond semiclassical approximation.