Statistical Entropy of Horowitz—Strominger Black Hole

The partition functions of bosonic and fermionic fields in Horowitz-Strominger black hole are derived directly by quantum statistical method.Then via the improved brick-wall method (membrane model),the statistical entropy of black hole is obtained.If a proper parameter is chosen in our result,it is found out that the entropy is proportional to the area of horizon.The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist.The difficulty in solving the wave equations of scalar and Dirac fields is avoided.A new neat way of calculating the entropy of various complicated black holes is offered.     

Quantum Statistical Entropy of Black Hole

By using the method of quantum statistics, we derive the partition function of bosonic and fermionic field in various coordinates and obtain the integral expression of the entropy of a black hole. Then via the improved brick-wall method, membrane model, we obtain that if we choose proper parameter, the entropy of black hole is proportional to the area of horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. We offer a new simple and direct way of calculating the entropy of black holes in various coordinates.     

The Quantum Entropy in Horowitz-Strominger Black Hole Background

Using 't Hooft's brick wall model and Newman-Penrose's spinor analysis, the expression of the quantum entropy is derived in the Horowitz-Strominger black hole background. The calculations show us that the Fermionic entropy is 7/2 times the Bosonic entropy.     

Statistical Entropy of Black Cylinder

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic fields in black cylinder. Then via the improved brick-wall method, membrane model, we obtain that if we choose the proper parameter, the entropy of black cylinder is proportional to the area of the horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, we do not take any approximation. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes: in Dirac Field Case

The total quantum statistical entropy of Reissner-Nordstrom black holes in Dirac field case is evaluated in this article. The space-time of the black holes is divided into three regions: region 1 (r>r_o), region 2 ( r_o > r > r_i), and region 3 (r_i >r>0), where r_o is the radius of the outer event horizon, and r_i is the radius of the inner event horizon. The total quantum statistical entropy of Reissner-Nordstrom black holes is S=S₁+S₂+S₃, where S_i (i=1,2,3) is the entropy, contributed by regions 1,2,3. The detailed calculation shows that S₂ is neglectfully small. S₁=w_t(π²/45)k_b(A_o/ε²β³), S₃=-w_t(π²/45)k_b(A_i/ε²β³), where A_o and A_i are, respectively, the areas of the outer and inner event horizons, w_t=2^s[1- 2^-(s+1)], s=d/2, d is the space-time dimension, here d=4, s=2. As r_i approaches r_o in the extreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approaches zero.     

Letter: Quantum Statistical Entropy of d-Dimensional Horowitz–Strominger Black Hole

By using the method of quantum statistics, we derive directly the partition functions of bosonic and fermionic field in the d-dimensional Horowitz-Strominger black hole. The statistical entropy of black hole is obtained by an improved brick—wall method. When we choose proper parameter in our results, we can obtain that the entropy of the black hole is proportional to the area of the horizon. In our result, there don't exist the left out term and divergent logarithmic term given in the original brick—wall method. We avoid the difficulty in solving the wave equation of scalar and Dirac field. And we offer a simple and direct way of studying entropy of the higher-dimensional complicated 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.     

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.     

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.     

Comments on the Statistical Origin of Black Hole Entropy

This paper shows that the black hole entropy can be interpreted as emerging as a result of missing information about the exact state of the matter from which the black hole was formed.     

Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation and other black hole radiated power is derived in terms of black hole density, ρ . Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy S _bh∝ (kAc ³)/ℏ G. Variations of S _bh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius R _H, p = which is similar tothe Compton wavelength relation.     

Entropy of Dilatonic Black Hole

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field in dilatonic black hole and obtain the integral expression of the black hole's entropy, which avoids the difficulty in solving the wave equationof various particles. Then via the improved brick-wall method, membrane model, we obtain that we can choose proper parameter in order to let the thickness of film tend to zero and have it approach the surface of its horizon. Consequently the entropy of the black hole is proportional to the area of its horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, physics idea is clear; calculation is simple. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length

Considering corrections to all orders in Planck length on the quantum state density from a generalized uncertainty principle （GUP）, we calculate the statistical entropy of the Bose field and Fermi field on the background of the four-dimensional spherically symmetric black holes without any cutoff. It is obtained that the statistical entropy is directly proportional to the area of horizon.     

Entropy Corrections to Three-Dimensional Black Holes and de Sitter Spaces

It has been shown that non-rotating black holes Recently study showed that thermal fluctuations would give in three or four dimensions possess a canonical entropy. rise to logarithmic corrections to Bekenstein Hawking entropy in area with a model-dependent uncertain coefficient. In this paper, the thermal fluctuations on Bekenstein-Hawking entropy in three-dimensional AdS black holes, Schwarzschild-de Sitter space and Kerr-de Sitter （KdS） spacetime with J = 0 will be considered based on a uniformly spaced area spectrum approach. Our conclusion shows that there is the same correction form in all cases we considered.     

Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length

Considering corrections to all orders in Planck length on the quantum state density from a generalized uncertainty principle (GUP), we calculate the statistical entropy of the Bose field and Fermi field on the background of the four-dimensional spherically symmetric black holes without any cutoff. It is obtained that the statistical entropy is directly proportional to the area of horizon.     

Entropy of N-Dimensional Spherically Symmetric Charged Black Hole

By using the method of quantum statistics, we derive directly the partition functions of bosonic andfermionic fields in the N-dimensional spherically symmetric charged black hole space-time. The statistical entropy ofblack hole is obtained by an improved brick-wall method. When we choose proper parameters in our results, we canobtain that the entropy of black hole is proportional to the area of horizon. In our result, there do not exist neglectedterm and divergent logarithmic term given in the original brick-wall method. We avoid the difficulty in solving the waveequation of scalar and Dirac fields. We offer a simple and direct way of studying entropy of the higher-dimensional black hole.     

The Entropy of Spherically Symmetric Black Holes Due to Arbitrary Spin Fields

Using the membrane model which is based on brick-wall model, we calculated the free energy and entropy of spherically symmetric black holes due to arbitrary spin. The result shows that the entropy of a scalar field and the entropy of a Fermionic field have similar formulas. There is only a coefficient between them.     

Entropy of Reissner—Nordstrom—De Sitter Black Hole in Nonthermal Equilibrium

By making use of the method of quantum statistics,we directly derive the partition function of bosonic and fermionic fields in Reissner-Nordstrom-De Sitter black Hole and obtain the integral expression of black hole‘s entropy and the entropy to which the cosmic horizon surface corresponds.It avoids the difficulty in solving the wave equation of various particles.Then via the improved brick-wall method,i.e.the membrane model,we calculate black hole‘s entropy and cosmic entropy and find out that if we let the integral upper limit and lower limit both tend to the horizon,the entropy of black hole is proportional to the area of horizon and the entropy to which cosmic horizon surface corresponds is proportional to the area of cosmic horizon.In our result,the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist.In the whole process,the physical idea is clear and the calculation is simple.We offer a new simple and direct way for calculating the entropy of different complicated black holes.     

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.     

LETTER: Entropy Using Path Integrals for Quantum Black Hole Models

Canonical quantum gravity has been used in the search for eigenvalue equations that could describe black holes. In this paper we choose one of the simplest of these quantum equations to show how the usual Feynman's path integral approach can be applied to get the corresponding statistical properties. We get a logarithmic correction to the Bekenstein–Hawking entropy as already obtained by other authors by other means.