The generalized uncertainty relation and the quantum entropy of static spherical black hole surrounded by quintessence due to spin fields

2016 ◽  
Vol 94 (10) ◽  
pp. 1080-1084 ◽  
Author(s):  
Guqiang Li
Keyword(s):  
Black Hole ◽  
Uncertainty Relation ◽  
Brick Wall ◽  
Wall Model ◽  
Dominant Term ◽  
Gravitational Fields ◽  
Brick Wall Model ◽  
Generalized Uncertainty Relation ◽  
Spin Fields ◽  
Free Case

By using the brick-wall model, the quantum entropies of static spherical black hole surrounded by quintessence due to the Weyl neutrino, electromagnetic, massless Rarita–Schwinger, and gravitational fields for the source-free case are investigated from a generalized uncertainty relation. It is shown that in addition to the usual quadratically and logarithmically divergent terms, there exist additional quadratic, biquadratic, and logarithmic divergences at ultraviolet σ → 0, which not only depend on the black hole characteristics but also on the spins of the fields and the gravity correction factor. These additional terms describe the contribution of the quantum fields to the entropy and the effect of gravitational interactions on it. After the smallest length scale is taken into account, we find that the contribution of the gravitational interactions to the entropy is larger than the usual dominant term and becomes a part of the whole dominant term, so it is very important and cannot be neglected.

EFFECT OF THE GENERALIZED UNCERTAINTY RELATION ON THE BLACK HOLE ENTROPY

2002 ◽  
Vol 17 (33) ◽  
pp. 2209-2219
Author(s):  
XIANG LI
Keyword(s):  
Black Hole ◽  
Uncertainty Relation ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Wall Model ◽  
Dirac Fields ◽  
Brick Wall Model ◽  
Generalized Uncertainty Relation ◽  
Klein Gordon ◽  
The Difference

The quantum entropies of the black hole, due to the massless Klein–Gordon and Dirac fields, are investigated by Rindler approximation. The difference from the brick wall model is that we take into account the effect of the generalized uncertainty relation on the state counting. The divergence appearing in the brick wall model is removed and the entropies proportional to the horizon area come from the contributions of the modes in the vicinity of the horizon. Here we take the units G=c=ℏ=kB=1.

BLACK HOLE ENTROPY INSIDE AND OUTSIDE THE BRICK WALL

2003 ◽  
Vol 18 (15) ◽  
pp. 2681-2687 ◽  
Author(s):  
WENBIAO LIU ◽  
YIWEN HAN ◽  
ZHOU'AN ZHOU
Keyword(s):  
Black Hole ◽  
Free Energy ◽  
Quantum Theory ◽  
Uncertainty Relation ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Wall Model ◽  
Horizon Area ◽  
Brick Wall Model ◽  
Generalized Uncertainty Relation

Applying the generalized uncertainty relation to the calculation of the free energy and entropy of a black hole inside the brick wall, the entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon. This is compared with the entropy calculated via the original brick wall model. The entropy given by the original brick wall model comes from the outside of the brick wall seemingly. The inside result using generalized uncertainty relation is similar to the outside result using original uncertainty relation, and the divergence inside the brick wall disappears. It is apparent that the cutoff is something related to the quantum theory of gravity.

IMPROVED BLACK HOLE ENTROPY CALCULATION WITHOUT CUTOFF

2004 ◽  
Vol 19 (09) ◽  
pp. 677-680 ◽  
Author(s):  
XUEFENG SUN ◽  
WENBIAO LIU
Keyword(s):  
Black Hole ◽  
Upper Bound ◽  
Uncertainty Relation ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Wall Model ◽  
Horizon Area ◽  
Brick Wall Model ◽  
Generalized Uncertainty Relation ◽  
Thin Film Model

The brick wall model and thin film model are most representative models in black hole entropy calculation. However, each of them must have a cutoff in order to avoid the divergence, and the divergence itself cannot be explained satisfactorily. Li Xiang6 substituted the classical uncertainty relation with the generalized uncertainty relation, the divergence was removed, consequently the cutoff was also removed. But due to the complex expression, he did not give the final solution. He only drew a conclusion that the upper bound of a black hole entropy is in proportional to its horizon area. The method using the generalized uncertainty relation to brick wall model is studied in depth. It is finally found out that the black hole entropy itself is also proportional to its horizon area instead of the upper bound.

WKB APPROXIMATION AND EFFECT OF SPIN ON THE BLACK HOLE ENTROPY

2007 ◽  
Vol 22 (28) ◽  
pp. 5229-5235 ◽  
Author(s):  
GU-QIANG LI
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Linear Term ◽  
Wkb Approximation ◽  
Quadratic Term ◽  
Brick Wall ◽  
Wall Model ◽  
Logarithmic Term ◽  
Brick Wall Model ◽  
Spin Fields

The black hole entropy due to spin fields are calculated by using brick-wall model. The appearance of the logarithmic terms is demonstrated and we specially deal with the subleading logarithmic term which exists for any spin fields. It is shown that the subleading logarithmic term is related to the use of WKB approximation but it usually includes not only a quadratic term and a linear term of the spin but also a zero-power term of the spin.

ENTROPY OF A NONSTATIC BLACK HOLE

2000 ◽  
Vol 15 (28) ◽  
pp. 1739-1747 ◽  
Author(s):  
LI XIANG ◽  
ZHAO ZHENG
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Time Dependent ◽  
Brick Wall ◽  
Two Dimensional ◽  
De Sitter ◽  
Wall Model ◽  
New Model ◽  
Brick Wall Model ◽  
Dynamical Degrees

We point out that the brick-wall model cannot be applied to the nonstatic black hole. In the case of a static hole, we propose a new model where the black hole entropy is attributed to the dynamical degrees of the field covering the two-dimensional membrane just outside the horizon. A cutoff different from the model of 't Hooft is necessarily introduced. It can be treated as an increase in horizon because of the space–time fluctuations. We also apply our model to the nonequilibrium and nonstatic cases, such as Schwarzschild–de Sitter and Vaidya space–times. In the nonstatic case, the entropy relies on a time-dependent cutoff.

THE ENTROPY OF A DIELECTRIC BLACK HOLE

2013 ◽  
Vol 28 (07) ◽  
pp. 1350009
Author(s):  
LICHUN ZHANG ◽  
HUAIFAN LI ◽  
REN ZHAO ◽  
RONGGEN CAI
Keyword(s):  
Black Hole ◽  
Correction Term ◽  
Entanglement Entropy ◽  
Constant Term ◽  
Logarithmic Correction ◽  
Brick Wall ◽  
Wall Model ◽  
Brick Wall Model ◽  
Black Hole Background ◽  
Dielectric Black Hole

In a dielectric black hole background, photons will be radiated via Hawking evaporation mechanism. In this paper, we calculate the entanglement entropy associated with a static dielectric black hole by employing 't Hooft's brick-wall model. It is found that the lowest energy of radiated particles is coordinate dependent. The resulted entanglement entropy is composed of three parts: a parameter independent leading constant term [Formula: see text], a logarithmic correction term and some series terms. The convergency of the series terms is also discussed.

ENTROPY OF A ROTATING AND ARBITRARILY ACCELERATING BLACK HOLE

2003 ◽  
Vol 12 (06) ◽  
pp. 1083-1094 ◽  
Author(s):  
XUEJUN YANG ◽  
YIWEN HAN ◽  
ZHENG ZHAO
Keyword(s):  
Thin Film ◽  
Black Holes ◽  
Black Hole ◽  
Surface Area ◽  
Entropy Density ◽  
Brick Wall ◽  
Total Entropy ◽  
Wall Model ◽  
Brick Wall Model ◽  
Nonstationary Black Hole

The entropy of a rotating and arbitrarily accelerating black hole whose metric changes slowly is calculated using the thin film brick-wall model. We obtain the entropy density at every point of the horizon surface and the total entropy of the black hole. The results show that the entropy of the nonstationary black hole is also proportional to the surface area of the black hole's event horizon as in the cases of stationary black holes.

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