Original Brick-wall Method Research Articles

Bekenstein–Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant λ introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein–Hawking entropy and the correction value corresponding cosmological horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein–Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.

Discussion of Garfinkle–Horowitz–Strominger Dilaton Black Hole Entropy

We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brickwall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bekenstein-Hawking's area-entropy formula. Then, by comparing with the original brick-wall method, we find that the result obtained by the thin film method is more reasonable avoiding some drawbacks, such as little mass approximation, neglecting logarithm term, and taking the term L3 as a contribution of the vacuum surrounding the black hole, and the physical meaning of the entropy is more clearer.

Rediscussion of charged dilaton-axion black hole entropy

Abstract We rediscuss the entropy of a charged dilaton-axion black hole for both the asymptotically flat and non-flat cases by using the thin film brick-wall model. This improved method avoids some drawbacks in the original brick-wall method such as the small mass approximation, neglecting the logarithm term, and taking the term L 3 as the contribution of the vacuum surrounding the black hole. The entropy we obtain turns out to be proportional to the horizon area of the black hole, conforming to the Bekenstein-Hawking area-entropy formula for black holes.

Quantum statistical entropy corresponding to cosmic horizon in five-dimensional spacetime

The generalized uncertainty relation is introduced to calculate the quantum statistical entropy corresponding to cosmic horizon. 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 five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is no divergent logarithmic term in the original brick-wall method. And it is obtained that the quantum statistical entropy corresponding to cosmic horizon is proportional to the area of the horizon. Further it is shown that the entropy corresponding to cosmic horizon 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. In our calculation, by using the quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of five-dimensional spacetime. We provide a way to study the quantum statistical entropy corresponding to cosmic horizon in the higher-dimensional spacetime.

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.

Quantum Statistic Entropy of Three-Dimensional BTZ Black Hole

Using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we investigate entropy of a black line on the background of the three-dimensional BTZ. In our calculation, we need not introduce cutoff and can remove the divergent term in the original brick-wall method via the new equation of state density. And it is obtained that the entropy of the black line is proportional to the area of the horizon (perimeter). Further it is shown the entropy of black line is the entropy of quantum state on the surface of horizon (perimeter). The black line entropy is the intrinsic property of the black hole. The entropy is a quantum effect. By using quantum statistical method, we directly obtain the partition function of Bose field and fermi field on the background of the black line. The difficulty to solve wave equation of various particles is avoided. We offer a new simple and direct way for calculating the entropy of various spacetime black holes (black plane, black line and black column).

Quantum Statistical Entropy of Five-Dimensional BlackHole

The generalized uncertainty relation is introduced to calculatequantum statistic entropy of a black hole. By using thenew equation of state density motivated by the generalizeduncertainty relation, we discuss entropies of Bose field and Fermifield on the background of the five-dimensional spacetime. In ourcalculation, we need not introduce cutoff. There is not thedivergent logarithmic term as in the original brick-wall method. Andit is obtained that the quantum statistic entropy corresponding toblack hole horizon is proportional to the area of the horizon.Further it is shown that the entropy of black hole is the entropy ofquantum state on the surface of horizon. The black hole's entropyis the intrinsic property of the black hole. The entropy is aquantum effect. It makes people further understand the quantum statistic entropy.

UNCERTAINTY RELATION AND BLACK HOLE ENTROPY OF TOROIDAL SPACETIME

By using the method of quantum statistics and via the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we avoid the difficulty of solving wave equation, and directly derive the partition functions of bosonic and fermionic field in Toroidal black hole. Then we calculate the entropies of bosonic and fermionic field near the black hole horizon on the background of a black hole. In our result, the divergent logarithmic term and ultraviolet cutoff in the original brick-wall method by which the black hole entropy was derived no longer exist. It is shown that the entropy of the black hole is proportional to the area of the horizon. These results are similar to that in the black hole with horizon topology S2.

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.

Bosonic and fermionic entropy of black holes with different temperatures on horizon surface

By using the method of quantum statistics, we derive directly the partition functions of bosonic and fermionic field in the black hole space–time with different temperatures on horizon surface. The statistical entropy of the black hole is obtained by an improved brick-wall method. When we choose a proper parameter in our results, we can obtain that the entropy of the black hole is proportional to the area of horizon. In our result, there do not exist any neglected term or divergent logarithmic term as given in the original brick-wall method. We have avoided the difficulty in solving the wave equation of the scalar and Dirac field. A simple and direct way of studying entropy of the black hole is given.

Statistical entropy of a rotating higher-dimensional black hole

By using the method of quantum statistics, we directly derive the partition function of the bosonic and the fermionic fields in the rotating (4 + n)-dimensional black hole and obtain an integral expression for the black hole's entropy. Then, via the improved brick-wall method, the membrane model, we obtain the statistical entropy of the black hole and find that we can choose a proper parameter in order to let the thickness of the film tend to zero and have it approach the surface of the horizon. Consequently, the entropy of the black hole is proportional to the area of the horizon. In our result, we also take the spinning degeneracy of various particles into consideration. The stripped term and the approximation taken in the original brick-wall method no longer exist. In the whole process, physics is clear, and the calculation is simple. We offer a new simple and direct way of calculating the entropy of the rotating higher-dimensional black holes.

Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole**The project supported by Natural Science Foundation of Shanxi Province of China

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 of N-Dimensional Spherically Symmetric Charged Black Hole**The project supported by the Shanxi Provincial Natural Science Foundation of China

By using the method of quantum statistics, we derive directly the partition functions of bosonic and fermionic fields in the N-dimensional spherically symmetric charged black hole space-time. The statistical entropy of black hole is obtained by an improved brick-wall method. When we choose proper parameters in our results, we can obtain that the entropy of black hole is proportional to the area of horizon. In our result, there do not exist neglected 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 fields. We offer a simple and direct way of studying entropy of the higher-dimensional black hole.

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.

Statistical Entropy of Horowitz–Strominger Black Hole**The project supported by Shanxi Natural Science Foundation of China and Foundation for the returned scholar from the Education Commission of Shanxi Province of China

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.

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.

Entropy of Reissner–Nordstrom–De Sitter Black Hole in Nonthermal Equilibrium**The project supported by Natural Science Foundation of Shanxi Province of China and by Foundation for the Returned Scholar from the Education Commission of Shanxi Province of China

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.

Entropy of Reissner-Nordström-anti-de Sitter black hole

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field in Reissner-Nordstrom-anti-de Sitter black hole and obtain the integral expression of black hole's entropy. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, membrane model, we calculate the statistical entropy of a film with the thickness of (N - 1)ξ around the outside of horizon. In our result we can choose proper parameter in order to let the thickness of film tend to zero and have it approach the surface of horizon. Consequently, the entropy of black hole is proportional to the area of horizon. 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 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.

THE ENTROPY CALCULATED VIA BRICK-WALL METHOD COMES FROM A THIN FILM NEAR THE EVENT HORIZON

The brick-wall method put forward by 't Hooft has contributed a great deal to the understanding and calculating of the entropy of a black hole. However, there are some drawbacks in it such as little mass approximation, neglecting logarithm terms, and taking the term including L3as a contribution of the vacuum surrounding the black hole. Moreover, the fundamental problem is why the entropy of scalar field or Dirac field surrounding a black hole is the entropy of the black hole itself. It is well known that the event horizon is the characteristic of a black hole. The entropy calculation of a black hole should be only related to its horizon. Due to this analysis, we improve the brick-wall model by taking that the entropy of a black hole is only contributed by a thin film near the event horizon. This improvement not only gives us a satisfied result, but also avoids the drawbacks in the original brick-wall method. It is found that there is an intrinsic relation between the event horizon and the entropy. We also calculate the entropy of Schwarzschild–de Sitter space–time via the improved method, which can hardly be resolved via the original model.