Wu Yueqin

Spherically symmetric black-hole entropy without brick walls

Properties of the thermal radiation of black holes are discussed using a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst at the last stage of emission from a spherically symmetric black hole. When the new equation of state density is used to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static spherically symmetric black hole, the divergence that appears in the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution from the vicinity of the horizon.

LETTER: The Nernst Theorem and the Entropy of the Reissner–Nordström Black Hole

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method on the background of the Reissner–Nordström black hole. We obtain the entropy of a scalar field is not only related to the location of an outer horizon but also is the function of the location of an inner horizon. In the approximation, the entropy is only proportional to the area of an outer horizon. The entropy expressed by location parameter of outer and inner horizon approaches zero, when the radiation temperature of a black hole approaches absolute zero. It satisfies the Nernst theorem.

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 holes entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.

Quantum statistical entropy for Kerr－de Sitter black hole

Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black holes entropy which contains two horizons (a black holes horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black holes horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black holes entropy and horizons area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.

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.

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 horizons 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*

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.

Black Hole and Cosmic Entropy for Schwarzschild–de Sitter Space–Time

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method in the background of the Schwarzschild–de Sitter space–time. We obtain the entropy of a black hole and the cosmic entropy at nonasymptotic flat space. When the cut-off satisfies the proper condition, the entropy of a black hole is proportional to the area of a black hole horizon, and the cosmic entropy is proportional to the cosmic horizon area.

Nernst Theorem and Entropy of the Axisymmetric Einstein–Maxwell–Dilaton-Axion Black Hole

The free energy and the entropy of scalar field are calculated by brick-wall in the axisymmetric Einstein–Maxwell–Dilaton-axion black hole. It is shown that when the black hole has inner and outer horizons, the entropy is not only related to the area of an outer horizon but also is the function of the area of an inner horizon. When the area of an inner horizon approaches zero, we can obtain the known conclusion. The entropy expressed by location parameter of outer horizon and inner horizons approaches absolute zero. It obeys Nernst theorem. It can be taken as Planck absolute entropy of a black hole.

QUANTUM THERMAL EFFECT OF NONSTATIC CHARGED BLACK HOLE

The difficulty of calculating energy-momentumtensors is avoided by finding directly the solution ofKlein–Gordon and Dirac equations near the horizon.Both the location of the event horizon and the Hawking radiation temperature of a nonstatic chargedblack hole are shown. The results indicate that theHawking radiation temperature can be regarded as acompensating effect under the timescaletransformation.