Immirzi parameter and quasinormal modes in four and higher spacetime dimensions

There is a one-parameter quantization ambiguity in loop quantum gravity, which is called the Immirzi parameter. In this paper, we fix this free parameter by considering the quasinormal mode spectrum of black holes in four and higher spacetime dimensions. As a consequence, our result is consistent with the Bekenstein–Hawking entropy of a black hole. Moreover, we also give a possible quantum gravity explanation of the universal ln 3 behavior of the quasinormal mode spectrum.     

Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole

We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes.     

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.     

Loop quantum gravity and black hole entropy quantization

Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity, the minimum horizon area gap is obtained. Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization. The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi. Supported by the National Natural Science Foundation of China (Grant No. 10773002)     

Gibbons-Maeda dilaton 黑洞的纠缠熵

按纠缠熵方法，计算了Gibbons-Maeda(G-M)dilaton黑洞视界外部与黑洞内量子态纠缠的一薄层内量子场的统计熵，得到了G-M dilaton黑洞的Bekenstein-Hawking熵.用广义不确定原理对量子态密度进行修正，克服了brick-wall模型中视界附近态密度的发散困难，该薄层可以紧贴在事件视界上.对brick-wall外部量子场中与黑洞内自由度有关联的自由度统计熵进行了计算，并把结果与brick-wall内量子场的熵进行比较分析，显示两结果具有与视界面积成正比的一致性，但后者能更 关键词： 纠缠熵 黑洞 广义不确定原理 截断     

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.     

Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data—the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2{{\mathcal N}=2} supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner–Nordstrom black holes in ordinary Einstein–Maxwell theory.     

Existence of a semiclassical approximation in loop quantum gravity

We consider a spherically symmetric black hole in the Schwarzschild metric and apply Bohr-Sommerfeld quantization to determine the energy levels. The canonical partition function is then computed and we show that the entropy coincides with the Bekenstein-Hawking formula when the maximal number of states for the black hole is the same as computed in loop quantum gravity, proving in this case the existence of a semiclassical limit and obtaining an independent derivation of the Barbero-Immirzi parameter.     

Holographic Entanglement Entropy of the BTZ Black Hole

We investigate quantum entanglement of gravitational configurations in 3D AdS gravity using the AdS/CFT correspondence. We derive explicit formulas for the holographic entanglement entropy (EE) of the BTZ black hole, conical singularities and regularized AdS₃. The leading term in the large temperature expansion of the holographic EE of the BTZ black hole reproduces exactly its Bekenstein-Hawking entropy S _BH , whereas the subleading term behaves as ln S _BH . We also show that the leading term of the holographic EE for the BTZ black hole can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. This result indicates that black hole EE is not a fundamental feature of the underlying theory of quantum gravity but emerges when the semiclassical notion of spacetime geometry is used to describe the black hole.     

Entropy of a Black Hole with Distinct Surface Gravities

In gravitational thermodynamics, the entropy of a black hole with distinct surface gravities can be evaluated in a microcanonical ensemble. At the WKB level, the entropy becomes the negative of the Euclidean action of the constrained instanton, which is the seed for the black hole creation in the no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite universal formula in Euclidean quantum gravity that the entropy of a nonrotating black hole is one quarter the sum of the products of the Euler characteristics and the areas of the horizons. For Lovelock gravity, the entropy and quantum creation of a black hole are also studied.     

Black Hole Entropy with Modified Dispersion Relations

There is much interest in resolving the quantum corrections to Bekenstein-Hawking entropy with a large length scale limit. The leading correction term is given by the logarithm of black hole area with a model-dependent coefficient. Recently the research for quantum gravity implies the emergence of a modification of theenergy-momentum dispersion relation (MDR), which plays an importantrole in the modified black hole thermodynamics. In this paper, we investigate the quantum corrections to Bekenstein-Hawking entropy in four-dimensional Schwarzschild black hole and Reissner-Nordström black hole respectively based on MDR.     

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.     

Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length

Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided. We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a non-spherical symmetric spacetime.     

Spectrum of a quantized black hole,correspondence principle,and holographic bound

An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either does not comply with the holographic bound or requires a special choice of the Barbero-Immirzi parameter for the horizon surface, distinct from its value for other quantized surfaces. The problem of distinguishability of the edges in LQG is discussed, with the following conclusion: Only under the assumption of partial distinguishability of the edges can the microcanonical entropy of a black hole be made both proportional to the horizon area and satisfying the holographic bound.     

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.     

量子史瓦茨黑洞和暗物质

引入Sommerfeld作用量量子化条件来处理Schwarzschild黑洞的量子化问题. 发现此类量子化黑洞存在一个质量为m_G=123m_p的基态，处于基态的量子Schwarzschild黑洞不再存在Hawking蒸发和任何其他辐射，可名之曰暗星. 它的存在不仅可以解决信息丢失的疑难，而且极可能是构成暗物质的主要候选者. 关键词： 量子史瓦茨黑洞 暗物质