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

2001 ◽  
Vol 16 (23) ◽  
pp. 3793-3803 ◽  
Author(s):  
WENBIAO LIU ◽  
ZHENG ZHAO
Keyword(s):  
Thin Film ◽  
Black Hole ◽  
Event Horizon ◽  
Fundamental Problem ◽  
Dirac Field ◽  
Brick Wall ◽  
De Sitter ◽  
Wall Model ◽  
Mass Approximation ◽  
Wall Method

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 L3 as 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.

ENTROPY OF SCHWARZSCHILD–de SITTER BLACK HOLE IN NON-THERMAL-EQUILIBRIUM

2001 ◽  
Vol 16 (11) ◽  
pp. 719-723 ◽  
Author(s):  
REN ZHAO ◽  
JUNFANG ZHANG ◽  
LICHUN ZHANG
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Thermal Equilibrium ◽  
Gordon Equation ◽  
Brick Wall ◽  
De Sitter ◽  
Logarithmic Term ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Wall Method

Starting from the Klein–Gordon equation, we calculate the entropy of Schwarzschild–de Sitter black hole in non-thermal-equilibrium by using the improved brick-wall method-membrane model. When taking the proper cutoff in the obtained result, we obtain that both black hole's entropy and cosmic entropy are proportional to the areas of event horizon. We avoid the logarithmic term and stripped term in the original brick-wall method. It offers a new way of studying the entropy of the black hole in non-thermal-equilibrium.

Rediscussion of charged dilaton-axion black hole entropy

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Chunyan Wang ◽  
Yuanxing Gui
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Small Mass ◽  
Brick Wall ◽  
Improved Method ◽  
Wall Model ◽  
Asymptotically Flat ◽  
Entropy Formula ◽  
Mass Approximation ◽  
Wall Method

AbstractWe 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.

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.

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.

Entropy of charged dilaton-axion black hole with minimal length revisited

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Chunyan Wang ◽  
Yuanxing Gui ◽  
Lili Xing
Keyword(s):  
Thin Film ◽  
Black Hole ◽  
Free Energy ◽  
Degrees Of Freedom ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Brick Wall ◽  
Wall Model ◽  
Asymptotically Flat ◽  
Brick Wall Model

AbstractUsing the generalized uncertainty principle, we calculate the entropy of the charged dilaton-axion black hole for both asymptotically flat and non-flat cases by counting degrees of freedom near the horizon. The divergence of density of states and free energy appearing in the thin film brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.

ENTROPY CALCULATION OF A KERR–NEWMAN BLACK HOLE VIA THE THIN FILM BRICK-WALL MODEL

2004 ◽  
Vol 19 (17n18) ◽  
pp. 3005-3011 ◽  
Author(s):  
ZHOU'AN ZHOU ◽  
WENBIAO LIU
Keyword(s):  
Thin Film ◽  
Black Hole ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Wall Model ◽  
Area Theorem ◽  
Brick Wall Model ◽  
Thin Film Model ◽  
Newman Black Hole ◽  
Different Temperatures

Applying the powerful thin film brick-wall model to the general Kerr–Newman black hole, we find out that the entropy calculation result can also satisfy the area theorem. Moreover, the area theorem is not only satisfied for the global black hole, but also for every area cell on its horizon, that means, every cell on the horizon contributes its own part of entropy if we choose a same temperature-related radial cutoff ε'. This new thin film brick-wall model can be used to calculate dynamic black hole which has different temperatures on the horizon. It tells us that the horizon is exactly the statistical origin of a black hole entropy, the total entropy of a black hole is just the sum of all the contributions from every area cell. For a Kerr–Newman black hole, there is also an important difference between the thin film brick-wall model and the original one, that is, we do not need any angular cutoff in the thin film model, and this makes the physical meaning clearer.

THE FERMIONIC ENTROPY OF SPHERICALLY SYMMETRIC BLACK HOLES

2000 ◽  
Vol 15 (31) ◽  
pp. 1901-1914 ◽  
Author(s):  
YOU-GEN SHEN
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Dirac Field ◽  
Spherically Symmetric ◽  
Brick Wall ◽  
Wall Model ◽  
Brick Wall Model ◽  
Black Hole Background ◽  
Symmetric Black Hole ◽  
Fermionic Entropy

The free energy and entropy for Dirac field is derived in the general spherically symmetric black hole background, by using 't Hooft's brick wall model. It is found that, in such a black hole background, fermionic entropy is 7/2 times the value of bosonic entropy.

COMPUTING THE ENTROPY OF KERR–NEWMAN BLACK HOLE WITHOUT BRICK WALLS METHOD

2008 ◽  
Vol 23 (20) ◽  
pp. 3155-3163 ◽  
Author(s):  
LI-CHUN ZHANG ◽  
YUE-QIN WU ◽  
HUAI-FAN LI ◽  
ZHAO REN
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Quantum States ◽  
Brick Wall ◽  
Wall Model ◽  
Brick Wall Model ◽  
Newman Black Hole

By using the entanglement entropy method, the statistical entropy of the Bose and Fermi fields in a thin film is calculated and the Bekenstein–Hawking entropy of Kerr–Newman black hole is obtained. Here, the Bose and Fermi fields are entangled with the quantum states in Kerr–Newman black hole and are outside of the horizon. The divergence of brick-wall model is avoided without any cutoff by the new equation of state density obtained with the generalized uncertainty principle. The calculation implies that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole. The black hole entropy is a quantum effect. It is an intrinsic characteristic of space–time. The ultraviolet cutoff in the brick-wall model is unreasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the calculation, the constant λ introduced in the generalized uncertainty principle is related to polar angle θ in an axisymmetric space–time.

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