Entropy in the NUT—Kerr—Newman Black Holes in the Background of de Sitter Spacetime

We calculate the entropy of the fermion field in the NUT-Kerr-Newman black holes in the background of the de Sitter spacetime by using the improved brick-wall method and the membrane model.Here the Euler characteristic of the black holes is over two.The results show that,as the cut-off is properly chosen,the entropy in the black hole satisfies the Bekenstein-Hawking area law.     

Entropy and topology of the Kerr—de Sitter black hole

By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole is investigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of the Euler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin of the entropy of the black hole is related to the topology of its instanton.     

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.     

Perturbation of Massive Scalar Field in Three—Dimensional Spherical de Sitter Space—time

We obtain exact expressions of quasi-normal modes in three-dimensional spherical de Sitter space-time,Exact agreement is found between the quasi-normal frequencies and the location of poles of the retarded correlation function of the corresponding perturbations in the dual conformal field theory.Our results exhibits the deSitter/conformal-field theory correspondence in three-dimensional spherical space-time.     

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 hole‘s entropy which contains two horizons (a black hole‘s horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole‘s 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 hole‘s entropy and horizon‘s area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.     

Entropy of Dirac Field in Non-stationary and Slowly Changing Reissner-Nordstrom Black Hole

Using the thin film brick-wall model and WKB approximation, the entropy of the Dirac field in the nonstationary and slowly changing Reissner-Nordstrom （R-N） black hole is calculated. The result shows that the entropy of the R-N black hole is still proportional to its surface area if we choose proper cut-off.     

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.     

Topological Aspects of Entropy and Phase Transition of Kerr Black Holest

In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem, it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime. By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4 for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.     

Hawking radiation of Kerr–Newman–de Sitter black hole

We extend the classical Damour–Ruffini method and discuss Hawking radiation in Kerr–Newman–de Sitter (KNdS) black hole. Under the condition that the total energy, angular momentum and charge of spacetime are conserved, taking the reaction of the radiation of the particle to the spacetime and the relation between the black hole event horizon and the cosmological horizon into consideration, we derive the black hole radiation spectrum. The radiation spectrum is no longer a pure thermal one. It is related to the change of the Bekenstein–Hawking entropy corresponding the black hole event horizon and the cosmological horizon. It is consistent with the underlying unitary theory.     

The Scalar Field Equation in Schwarzschild–de Sitter Space

The scalar wave equation between the inner and the outer horizon in the Schwarzschild–de Sitter geometry is solved numerically, and the spatial variations of the field amplitude, as well as of the potential, are shown graphically. By generalizing the "tortoise" coordinate x known from Schwarzschild theory to the SdS system we first transfer the wave equation to a convenient form in which the potential V is written as a function of x. We then show how a useful "tangent" approximation can be introduced which leads to a simple, analytically invertible, relation between x and the radius r. We concentrate on two limiting cases. The first case is when the two horizons are close to each other, the so-called Nariai black hole, and the second case is when the horizons are far apart. Reflection and transmission coefficients are worked out on the basis of a replacement of the real barrier V(x) by a square barrier.     

Quantization of Horizon Area of Kerr–Newman–de Sitter Black Hole

Using the adiabatic invariant action and applying the Bohr–Sommerfeld quantization rule and first law of black hole thermodynamics, a study of the quantization of the entropy and horizon area of a Kerr–Newman–de Sitter black hole is carried out. The same entropy spectrum is obtained in two different coordinate systems. It is also observed that the spacing of the entropy spectrum is independent of the black hole parameters. Also, the corresponding quantum of horizon area is in agreement with the results of Bekenstein.     

Quantum Radiation of a Non-stationary Kerr-Newman Black Hole in de Sitter Space-Time

Hawking radiation of Klein-Gordon and Dirac particles in a non-stationary Kerr-Newman-de-Sitter black hole is studied by introducing a new tortoise coordinate transformation. The result shows that the Fermi-Dirac radiant spectrum displays a new term that represents the interaction between the spin of spinor particles and the rotation of black holes, which is absent in the Bose-Einstein distribution of Klein-Gordon particles.     

Quantum radiation of non-stationary Kerr－Newman－de Sitter black hole

By introducing a new tortoise coordinate transformation, we investigate the quantum thermal and non-thermal radiations of a non-stationary Kerr--Newman--de Sitter black hole. The accurate location and radiate temperature of the event horizon as well as the maximum energy of the non-thermal radiation are derived. It is shown that the radiate temperature and the maximum energy are related to not only the evaporation rate, but also the shape of the event horizon, moreover the maximum energy depends on the electromagnetic potential. Finally, we use the results to reduce the non-stationary Kerr--Newman black hole, the non-stationary Kerr black hole, the stationary Kerr--Newman--de Sitter black hole, and the static Schwarzshild black hole.     

The First Law of Thermodynamics of the （2＋1）-Dimensional Banados-Teitelboim-Zanelli Black Holes and Kerr-de Sitter Spacetimes

We investigate the first law of thermodynamics in the case of the （2 ＋ 1）-dimensional Banados Teitelboim-Zanelli black holes and Kerr-de Sitter spacetimes. In particular, we focus on the integral mass formulas. It is found that by assuming the cosmological constant as a variable state parameter, both the differential and integral mass formulas of the first law of black hole thermodynamics in the asymptotic fiat spacetimes can be directly extended to those of rotating black holes in anti-de Sitter and de Sitter backgrounds. It should be pointed that these formulae come into existence in any dimensions.     

Scalar Field at the Phase Transition Point of RNdS Space

The real scalar field equation between the outer black hole horizon and the cosmological horizon is solved in the Reissner-Nordstroem-de Sitter space when it is at the phase transition point. We use an accurate approximation,the polynomial approximation, to approximate the tortoise coordinate x(r) for obtaining the inverse function r=r(x) and then for solving the wave equation. The case where the two horizons are very close to each other is discussed in detail. It is found that the wave function is characteristically similar to the harmonic in the whole range with x as the independent coordinate, while the waves pile up near the horizons with r as the independent coordinate. Furthermore, we find that the height of the potential increases as the cosmological constant A decreases.     

De Broglie—Bohm Quantization of the Reissner—Nordstrom Black Hole with a Global Monopole in the Background of de Sitter Space—Time

We present the classical solution of Lagrange equations for the Resissner-Nordstrom black hole with a global monopole in the background of de Sitter space-time.Then we obtain the wavefunction of the space-time by solving the Wheeler-De Witt equation.De Broglie-Bohm interpretation applied to the wavefunction gives the quantum solution of the space-time.Finally,the quantum effect on hawking radiation is studied.     

Distribution Characteristics of Dirac Energy Levels in Non—Kerr Space—time

The distribution of Dirac energy levels in a non-Kerr black hole space-time is related to an arbitrary set of multiple monents determined by the parameters αn.A singular point appears on the event horizon of the black hole ,at which the Dirac energy levels have obvious distribution characteristics and are different from those in the space-time of the Kerr black hole.     

Entropy of the Dirac Field in Schwarzschild–de Sitter Space-Time via the Membrane Model

There are two event horizons in Schwarzschild–de Sitter space-time, a blackhole horizon and a cosmological horizon. They have different temperatures. Theradiation between them is of course not in thermal equilibrium. According to themembrane model suggested by us, the two horizons can be thought of as twoindependent thermodynamic systems in equilibrium. Their Dirac field entropiesare calculated via a membrane model. The result shows that the entropy of theDirac field is proportional to the sum of the areas of the two event horizons. Ifwe choose the same cutoff as that of Klein–Gordon field, the entropy of theDirac field is times that of Klein–Gordon field. This agrees with previousresults.     

Hawking radiation of Weyl neutrinos in a rectilinearly non—uniformly accelerating Kinnersley black hole

The quantum thermal effect of Weyl neutrinos in a rectilinearly non-uniformly accelerating Kinnersley black hole is investigated using the generalized tortoise coordinate transformation.The equations that determine the location,the Hawking temperature of the event horizon and the thermal radiation spectrum of neutrinos are derived.Our results show that the location and the temperature of the event horizon depend not only on the time but also on the angle.