Rediscussion of charged dilaton-axion black hole entropy

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x01003524 ◽

2001 ◽

Vol 16 (23) ◽

pp. 3793-3803 ◽

Cited By ~ 12

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.

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BLACK HOLE ENTROPY BY THE BRICK-WALL METHOD IN FOUR AND FIVE DIMENSIONS WITH U(1) CHARGES

Modern Physics Letters A ◽

10.1142/s0217732301004960 ◽

2001 ◽

Vol 16 (39) ◽

pp. 2495-2503 ◽

Cited By ~ 7

Author(s):

ELCIO ABDALLA ◽

L. ALEJANDRO CORREA-BORBONET

Keyword(s):

Black Holes ◽

Black Hole ◽

Scalar Field ◽

Black Hole Entropy ◽

Brick Wall ◽

Statistical Entropy ◽

Five Dimensions ◽

Entropy Formula ◽

Wall Method

Using the brick-wall method we compute the statistical entropy of a scalar field in a nontrivial background, in two different cases. These backgrounds are generated by four- and five-dimensional black holes with four and three U(1) charges respectively. The Bekenstein entropy formula is generally obeyed, but corrections are discussed in the latter case.

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ENTROPY OF A NONSTATIC BLACK HOLE

Modern Physics Letters A ◽

10.1142/s0217732300001973 ◽

2000 ◽

Vol 15 (28) ◽

pp. 1739-1747 ◽

Cited By ~ 5

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.

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BOUND OF NONCOMMUTATIVITY PARAMETER BASED ON BLACK HOLE ENTROPY

Modern Physics Letters A ◽

10.1142/s0217732310034237 ◽

2010 ◽

Vol 25 (38) ◽

pp. 3213-3218 ◽

Cited By ~ 6

Author(s):

WONTAE KIM ◽

DAEHO LEE

Keyword(s):

Black Hole ◽

Gauge Group ◽

Black Hole Entropy ◽

Brick Wall ◽

Statistical Entropy ◽

Schwarzschild Black Hole ◽

Cutoff Parameter ◽

Entropy Satisfying ◽

Area Law ◽

Wall Method

We study the bound of the noncommutativity parameter in the noncommutative Schwarzschild black hole which is a solution of the noncommutative ISO(3, 1) Poincaré gauge group. The statistical entropy satisfying the area law in the brick wall method yields a cutoff relation which depends on the noncommutativity parameter. Requiring both the cutoff parameter and the noncommutativity parameter to be real, the noncommutativity parameter can be shown to be bounded as Θ > 8.4 × 10-2lp.

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EFFECT OF THE GENERALIZED UNCERTAINTY RELATION ON THE BLACK HOLE ENTROPY

Modern Physics Letters A ◽

10.1142/s0217732302008848 ◽

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.

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Effects of Noncommutativity on the Black Hole Entropy

Advances in High Energy Physics ◽

10.1155/2014/139172 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 12

Author(s):

Kumar S. Gupta ◽

E. Harikumar ◽

Tajron Jurić ◽

Stjepan Meljanac ◽

Andjelo Samsarov

Keyword(s):

Black Hole ◽

Scalar Field ◽

Deformation Parameter ◽

Black Hole Entropy ◽

Brick Wall ◽

Btz Black Hole ◽

First Order ◽

Hole Geometry ◽

Wall Method

The BTZ black hole geometry is probed with a noncommutative scalar field which obeys theκ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity.

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THE QUANTUM CORRECTIONS TO THE ENTROPY OF ROTATING U(1) ⊗ U(1)-DILATON BLACK HOLES

Modern Physics Letters A ◽

10.1142/s0217732399000286 ◽

1999 ◽

Vol 14 (04) ◽

pp. 239-246 ◽

Cited By ~ 13

Author(s):

YOU-GEN SHEN ◽

DA-MING CHEN

Keyword(s):

Black Holes ◽

Black Hole ◽

Black Hole Entropy ◽

Quantum Corrections ◽

Brick Wall ◽

Wall Model ◽

Brick Wall Model ◽

Dilaton Black Hole ◽

Massless Quantum ◽

Dilaton Black Holes

By using 't Hooft's brick wall model, the corrections for a massless quantum scalar field to the black hole entropy are studied in rotating U (1) ⊗ U (1)-dilaton black hole space–time. The free energy and entropy for this case are calculated, and in Hartle–Hawking states, the derived quantum entropy is composed of the geometric part and the non-geometric part which is logrithmically divergent. It turns out that the logrithmic part is related to the characteristic quantities of a black hole.

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BLACK HOLE ENTROPY INSIDE AND OUTSIDE THE BRICK WALL

International Journal of Modern Physics A ◽

10.1142/s0217751x03013673 ◽

2003 ◽

Vol 18 (15) ◽

pp. 2681-2687 ◽

Cited By ~ 12

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.

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

Open Physics ◽

10.2478/s11534-008-0151-9 ◽

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.

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