Quantum Black Hole

Creation of a black hole in quantum cosmology is the third way of black hole formation. In contrast to the gravitational collapse from a massive body in astrophysics or from the quantum fluctuation of matter fields in the very early universe, in the quantum cosmology scenario the black hole is essentially created from nothing. The black hole originates from a constrained gravitational instanton. The probability of creation for all kinds of single black holes in the Kerr-Newman family, at the semiclassical level, is the exponential of the total entropy of the universe, or one quarter of the sum of both the black hole and the cosmological horizon areas. The de Sitter spacetime is the most probable evolution at the Planckian era.     

Information Conservation in a Noncommutative Quantum Black Hole Based on Canonical Typicality*

A method for calculating the radiation spectrum of an arbitrary black holes was recently proposed by Ma et al., [Europhys. Lett. 122 (2018) 30001] in which a non-thermal spectrum of a black hole can be obtained from its entropy using an approach based on canonical typicality. The non-thermal spectrum of a black hole enables a nonzero correlation between the black hole and its radiation, which can ensure that information is conserved during black hole evaporation. In this paper, by using the Kantowski-Sachs metric and Feynman-Hibbs procedure, the entropy of a noncommutative quantum black hole is calculated based on the Wheeler-DeWitt equation. Then, the radiation spectrum of the noncommutative quantum black hole is studied based on canonical typicality method. At last, the correlation between the radiation spectra is calculated. It is shown that the noncommutative effect increases the correlation among radiation and the information remains conserved for noncommutative quantum black holes.     

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.     

An interpretation for the entropy of a black hole

We investigate the meaning of the entropy carried away by Hawking radiations from a black hole. We propose that the entropy for a black hole measures the uncertainty of the information about the black hole forming matter’s precollapsed configurations, self-collapsed configurations, and inter-collapsed configurations. We find that gravitational wave or gravitational radiation alone cannot carry all information about the processes of black hole coalescence and collapse, while the total information locked in the hole could be carried away completely by Hawking radiation as tunneling.     

Generalized Uncertainty Relation and Hawking Radiation of the Black Hole

Recently, there has been much attention devoted to the correction to the black hole radiation spectrum and the quantum corrections to Bekenstein-Hawking entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the radiation spectrum of arbitrary dimension Schwarzschild black hole after considering the generalized uncertainty principle. The correction value of Bekenstein-Hawking entropy is derived.     

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.     

Kerr Black Hole Entropy and its Quantization

By constructing the four-dimensional phase space based on the observable physical quantity of Kerr black hole and gauge transformation, the Kerr black hole entropy in the phase space was obtained. Then considering the corresponding mechanical quantities as operators and making the operators quantized, entropy spectrum of Kerr black hole was obtained. Our results show that the Kerr black hole has the entropy spectrum with equal intervals, which is in agreement with the idea of Bekenstein. In the limit of large event horizon, the area of the adjacent event horizon of the black hole have equal intervals. The results are in consistent with the results based on the loop quantum gravity theory by Dreyer et al.     

Quantization of Kerr-Newman Black Hole Entropy

Kerr-Newman black hole entropy in phase space is systematically investigated by constructing the six-dimensional phase space within gauge transformation. Then considering the corresponding mechanical quantities as operators and making them quantized, entropy spectrum of Kerr-Newman black hole is obtained. Our results demonstrate that Kerr-Newman black hole has an equal-interval entropy spectrum, which coincides with the view of Bekenstein. It also shows that Kerr-Newman black hole entropy is not zero, but exists a ground-state entropy, which still retains some basic information.     

Canonical Entropy of Black Hole in the Generalized Uncertainty Principle

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, based on the correction to black hole thermodynamic quantity due to the generalized uncertainty principle, we calculate the partition function by energy spectrum obtained using tunneling effect. Furthermore we derive the black hole entropy. In the expression, we not only consider the generalized uncertainty principle but also consider the departure of black hole radiation spectrum from pure thermal spectrum. According to criterion law of thermodynamic systems phase transition, we discuss the phase transition of AdS black hole and derive that the phase transition of AdS black hole is a secondary one.     

Black hole spectroscopy via adiabatic invariance

During the last years, one had to combine the proposal about how quasinormal frequencies are related with black holes and the proposal about the adiabatic invariance of black holes in order to derive the quantized entropy spectrum and its minimum change for several black holes. In this Letter we exclusively utilize the statement that the black hole horizon area is an adiabatic invariant and derive an equally spaced entropy spectrum of a black hole with its quantum to be equal to the one given by Bekenstein. Interestingly, in our approach no concept of quasi-normal mode is needed.     

Quantum corrections to the spectroscopy of a BTZ black hole via periodicity

Quantum corrections to the area spectrum and the entropy spectrum of a BTZ black hole are calculated by equaling the motion period of an outgoing wave coming from the quantum corrections of the semiclassical action to the period of gravitational system with respect to the Euclidean time. We find that the area spectrum and the entropy spectrum are independent of the properties of particles. Furthermore, in the presence of higher-order quantum corrections, the area spectrum is found to be corrected by inverse area terms while the entropy spectrum is found to have a universal form, $\varDelta S_{BH}=2\pi $ . Both results show that the entropy spectrum is independent of not only the BTZ black hole parameters but also the higher-order quantum corrections, which implies that the entropy spectrum is more natural than the area spectrum in quantum gravity theory.     

Quantum Statistical Entropy of Five-Dimensional Black Hole

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the 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. It makes people further understand the quantum statistic entropy.     

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.     

Black Holes and Inflation

A model for black hole collapse and evaporation in which the black hole is supposed to be an excited state of one of the Planck black holes pervading the structure of spacetime is discussed. By assuming a Coleman-Weinberg gravitational effective potential for a scalar field inside the collapse matter, it is shown that the black hole state cannot be attained neither through bubble tunneling nor by the rolling down of the field.     

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 spaeetime. 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 thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild 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 noneommutativity 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.     

Black hole mass threshold from nonsingular quantum gravitational collapse

Quantum gravity is expected to remove the classical singularity that arises as the end state of gravitational collapse. To investigate this, we work with a toy model of a collapsing homogeneous scalar field. We show that nonperturbative semiclassical effects of loop quantum gravity cause a bounce and remove the black hole singularity. Furthermore, we find a critical threshold scale below which no horizon forms: quantum gravity may exclude very small astrophysical black holes.     

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.     

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.     

Canonical Entropy of Reissner-Nordstrom Black Hole

Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How the departure from pure thermal spectrum affects the entropy? This is a very interesting problem. In this paper, we calculate the partition function by energy spectrum obtained by tunnel effect. Using the relation between the partition function and entropy, we derive the expression of entropy the general charged black hole. In our calculation, we not only consider the correction to the black hole entropy due to fluctuation of energy but also consider the effect of the change of the black hole charges on entropy. We discuss Reissner-Nordstrom black hole and obtain that Reissner-Nordstrom black hole cannot approach the extreme black hole by changing its charges.     

Black holes and information theory

During the past three decades investigators have unveiled a number of deep connections between physical information and black holes whose consequences for ordinary systems go beyond what has been deduced purely from the axioms of information theory. After a self-contained introduction to black hole thermodynamics, we review from its vantage point topics such as the information conundrum that emerges from the ability of incipient black holes to radiate, the various entropy bounds for non-black hole systems (holographic bound, universal entropy bound, etc.) which are most easily derived from black hole thermodynamics, Bousso's covariant entropy bound, the holographic principle of particle physics, and the subject of channel capacity of quantum communication channels.