Planck Absolute Entropy Research Articles

Planck absolute entropy of a rotating BTZ black hole

In this paper, the Planck absolute entropy and the Bekenstein–Smarr formula of the rotating Banados–Teitelboim–Zanelli (BTZ) black hole are presented via a complex thermodynamical system contributed by its inner and outer horizons. The redefined entropy approaches zero as the temperature of the rotating BTZ black hole tends to absolute zero, satisfying the Nernst formulation of a black hole. Hence, it can be regarded as the Planck absolute entropy of the rotating BTZ black hole.

Negative Temperature of Inner Horizon and Planck Absolute Entropy of a Kerr-Newman Black Hole

Considering the contribution of both the outer and inner horizons, the Hamilton–Jacobi method is applied to a Kerr–Newman black hole and a negative temperature of the inner horizon is obtained. Under the negative temperature inside the black hole, the thermodynamics of the two horizons is studied, and the new Bekenstein–Smarr formula is given. The entropies of the inner and outer horizons are all positive. The new entropy expression of the black hole satisfies the Nernst Theorem and can be regarded as the Planck absolute entropy.

Nernst theorem and Hawking radiation from a Reissner-Nordstrom black hole

The thermal character of inner horizon in a Reissner-Nordstrom black hole is studied via Hamilton-Jacobi method. There is “Hawking absorption” as a quantum effect near the inner horizon, and a negative temperature of the inner horizon was attained by choosing an observer outside the black hole. Using a redefined entropy of the black hole, we give a new expression of Bekenstein-Smarr formula. The redefined entropy satisfies Nernst Theorem, so it can be regarded as Planck absolute entropy of the Reissner-Nordstrom black hole.

Hawking Absorption and Planck Absolute Entropy of Kerr-Newman Black Hole

We find the existence of a quantum thermal effect, “Hawking absorption.” near the inner horizon of the Kerr–Newman black hole. Redefining the entropy, temperature, angular velocity, and electric potential of the black hole, we give a new formulation of the Bekenstein–Smarr formula. The redefined entropy vanishes for absolute zero temperature of the black hole and hence it is interpreted as the Planck absolute entropy of the KN black hole.

Planck absolute entropy of Demianski–Newman black holes

We investigate the thermal character of the inner horizon of the Demianski–Newman black hole and find the existence of a quantum thermal effect, “Hawking absorption”, near the inner horizon. We redefine the entropy, temperature, and angular velocity of the black hole and give a new formulation of the Bekenstein–Smarr formula in terms of these variables. The redefined entropy as well as the redefined temperature vanish for absolute zero temperature of the black hole. This leads to interpret the new entropy as the Planck absolute entropy of the DN black hole.

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.

THE ENTROPY OF A KIM BLACK HOLE AND THE NERNST THEOREM

We start with Klein-Gordon equation on the background of the Kim-black hole and calculate the free energy and entropy of a scalar field by the-brick-wall method. It is shown that the entropy is not only related to the area of an outer horizon but also is a function of inner horizon's area. Taking some appr oximation, we can obtain that the entropy only is proportional to the area of an outer horizon. Further more, the entropy expressed by location parameter of the outer and inner horizon approaches zero, when the radiation temperature of a black hole approaches zero. This satisfies the Nernst theorem. It can be taken as Planck absolute entropy of a black hole.

THE NERNST THEOREM AND STATISTICAL ENTROPY OF THE SCALAR FIELD IN REISSNER-NORDSTROM GEOMETRY

Based on the Klein-Gordon equations on the background of the Reisser-Nordstrom spacetime, we calculate the free energy and entropy of a scalar field near a black hole by improved brick-wall methodmembrane model. It is obtained that the entropy of the scalar field consists of two parts. As the entropy is an extensive quantity, we obtain that the black hole entropy comes from two thermodynamical systems. And the new Bekenstein-Smarr formula is given. It is shown that the entropy expressed by two thermodynamical subsystems approaches zero when the radiation temperature of the black hole approaches absolute zero. This obeys Nernst theorem. It can be taken as Planck absolute entropy of a black hole.

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.

THE NERNST THEOREM AND THE ENTROPY OF A CYLINDRICAL BLACK HOLE

Under nonspherical coordinates, the free energy and the entropy of a scalar field are calculated in terms of the brick-wall method on the background of a nonasymptotically flat cylindrical black hole. It is shown that the entropy is not only related to the area of an outer horizon but also function of inner horizon at nonasymptotically flat space–time, when a black hole has both inner and outer horizons. Further, the entropy expressed by location parameter of outer and inner horizons approaches zero, when the radiation temperature of a black hole approaches zero. It satisfies the Nernst theorem and can be taken as Planck absolute entropy of a black hole.

NERNST THEOREM AND PLANCK ABSOLUTE ENTROPY OF BLACK HOLE

After considering thermal character of the inner horizon of Kerr black hole, we give a new form of the Bekenstein-Smarr formula and re-define black hole entropy. The balck hole entropy re-defined must go to zero as the temperature of black the approaches absolute zero. The entropy satisfies the Nernst theorem, so it can be regarded as the Planck absolute entropy of black hole.

Planck Absolute Entropy of the Kerr Black Hole

The thermal character of the inner horizon ofthe Kerr black hole is studied. There is a quantumthermal effect, “Hawking absorption,” nearthe inner horizon. We give a new formulation of the Bekenstein-Smarr formula and redefine theentropy of the black hole. The redefined entropy must goto zero as the temperature of the black hole approachesabsolute zero. The entropy satisfies the Nernst theorem, so it can be regarded as the Planckabsolute entropy of the Kerr black hole.