scholarly journals Black Hole Entropy: A Closer Look

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 17 ◽  
Author(s):  
Constantino Tsallis
Keyword(s):  
Complex System ◽  
Black Hole ◽  
Event Horizon ◽  
Black Hole Entropy ◽  
Planck Length ◽  
Horizon Area ◽  
C 73 ◽  
Area Law

In many papers in the literature, author(s) express their perplexity concerning the fact that the ( 3 + 1 ) black-hole ‘thermodynamical’ entropy appears to be proportional to its area and not to its volume, and would therefore seemingly be nonextensive, or, to be more precise, subextensive. To discuss this question on more clear terms, a non-Boltzmannian entropic functional noted S δ was applied [Tsallis and Cirto, Eur. Phys. J. C 73, 2487 (2013)] to this complex system which exhibits the so-called area-law. However, some nontrivial physical points still remain open, which we revisit now. This discussion is also based on the fact that the well known Bekenstein-Hawking entropy can be expressed as being proportional to the event horizon area divided by the square of the Planck length.

scholarly journals BOUND OF NONCOMMUTATIVITY PARAMETER BASED ON BLACK HOLE ENTROPY

2010 ◽  
Vol 25 (38) ◽  
pp. 3213-3218 ◽  
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.

scholarly journals THERMODYNAMICS OF BLACK HOLE IN (N+3) DIMENSIONS FROM EUCLIDEAN N-BRANE THEORY

1995 ◽  
Vol 10 (36) ◽  
pp. 2775-2782 ◽  
Author(s):  
ICHIRO ODA
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Three Dimensional ◽  
Black Hole Entropy ◽  
Particle Model ◽  
Field Equations ◽  
3 Dimensional ◽  
The Past ◽  
Dimensional Black Hole ◽  
Brane Theory

In this letter we consider an N-brane description of an (N+3)-dimensional black hole horizon. First of all, we start by examining in more detail a previous work where a string theory is used in describing the dynamics of the event horizon of a four-dimensional black hole. This is an attempt to understand the black hole thermodynamics by an effective two-dimensional field theory of the event horizon of a black hole. Then we consider a particle model defined on one-dimensional Euclidean line in a three-dimensional black hole as a target spacetime metric. By solving the field equations we find a “worldline instanton” which connects the past event horizon with the future one. This solution gives us the exact value of the Hawking temperature and to leading order the Bekenstein-Hawking formula of black hole entropy. We also show that this formalism is extensible to an arbitrary spacetime dimension. Finally we make a comment of many recent works of one-loop quantum correction to the black hole entropy.

scholarly journals HOLOGRAPHY, GAUGE-GRAVITY CONNECTION AND BLACK HOLE ENTROPY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3414-3425 ◽  
Author(s):  
PARTHASARATHI MAJUMDAR
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Black Hole Entropy ◽  
Cross Sectional ◽  
Gauge Gravity ◽  
Thermal Stability Of ◽  
Spacetime Fluctuations ◽  
Area Law ◽  
Quantum Spacetime

The issues of holography and possible links with gauge theories in spacetime physics is discussed, in an approach quite distinct from the more restricted AdS-CFT correspondence. A particular notion of holography in the context of black hole thermodynamics is derived (rather than conjectured) from rather elementary considerations, which also leads to a criterion of thermal stability of radiant black holes, without resorting to specific classical metrics. For black holes that obey this criterion, the canonical entropy is expressed in terms of the microcanonical entropy of an Isolated Horizon which is essentially a local generalization of the very global event horizon and is a null inner boundary of spacetime, with marginal outer trapping. It is argued why degrees of freedom on this horizon must be described by a topological gauge theory. Quantizing this boundary theory leads to the microcanonical entropy of the horizon expressed in terms of an infinite series asymptotic in the cross-sectional area, with the leading 'area-law' term followed by finite, unambiguously calculable corrections arising from quantum spacetime fluctuations.

scholarly journals Power law corrections to BTZ black hole entropy

2014 ◽  
Vol 24 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Dharm Veer Singh
Keyword(s):  
Black Hole ◽  
Excited State ◽  
Power Law ◽  
Ground State ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Mixed States ◽  
Btz Black Hole ◽  
First Excited State ◽  
Area Law

We study the quantum scalar field in the background of BTZ black hole and evaluate the entanglement entropy of the nonvacuum states. The entropy is proportional to the area of event horizon for the ground state, but the area law is violated in the case of nonvacuum states (first excited state and mixed states) and the corrections scale as power law.

scholarly journals Where are the degrees of freedom responsible for black-hole entropy?

2008 ◽  
Vol 86 (4) ◽  
pp. 653-658 ◽  
Author(s):  
S Das ◽  
S Shankaranarayanan ◽  
S Sur
Keyword(s):  
Black Hole ◽  
Excited State ◽  
Power Law ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Black Hole Entropy ◽  
Quantum Field ◽  
Hole Area ◽  
Area Law ◽  
03.65 Ud

Considering the entanglement between quantum field degrees of freedom inside and outside the horizon as a plausible source of black-hole entropy, we address the question: where are the degrees of freedom that give rise to this entropy located? When the field is in ground state, the black-hole area law is obeyed and the degrees of freedom near the horizon contribute most to the entropy. However, for excited state, or a superposition of ground state and excited state, power-law corrections to the area law are obtained, and more significant contributions from the degrees of freedom far from the horizon are shown.PACS Nos.: 04.60.–m, 04.62., 04.70.–s, 03.65.Ud

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.

Event horizon area in a slowly changing Weyl geometry

1982 ◽  
Vol 60 (8) ◽  
pp. 1155-1162
Author(s):  
B. E. Brumbaugh ◽  
Richard H. Price
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Mathematical Description ◽  
Time Scale ◽  
Event Horizons ◽  
Weyl Geometry ◽  
Horizon Area ◽  
Slow Evolution ◽  
Horizon Geometry

We consider a class of models of dynamically distorted black hole event horizons, based on a slow evolution of black hole Weyl geometries. With the time scale for the evolution taken arbitrarily large, a fairly simple mathematical description of the "quasistatic" geometry results. With this description it is shown how the constraint on event horizon area is related to the absence of singularities at the horizon. The evolution of intrinsic event horizon geometry is plotted for a specific example.

A SCHRÖDINGER BLACK HOLE AND ITS ENTROPY

2002 ◽  
Vol 17 (15n17) ◽  
pp. 1047-1057 ◽  
Author(s):  
DANIEL SUDARSKY
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Event Horizon ◽  
Black Hole Entropy ◽  
A Value ◽  
The Future ◽  
Quantum Event ◽  
Quantum Variable ◽  
The Given

We discuss the conditions under which one can expect to have the usual identification of black hole entropy with the area of the horizon. We then construct an example in which the actual presence of the event horizon on a given hypersurface depends on a quantum event in which a certain quantum variable acquires a value and which occurs in the future of the given hypersurface. This situation indicates that there is something fundamental that is missing in the most popular of the current approaches towards the construction of a theory of quantum gravity, or, alternatively, that there is something fundamental that we do not understand about entropy in general, or at least in its association with black holes.

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