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

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.

SIGNATURES OF AN EMERGENT GRAVITY FROM BLACK HOLE ENTROPY

2009 ◽  
Vol 18 (14) ◽  
pp. 2323-2327
Author(s):  
CENALO VAZ
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Mass Spectrum ◽  
Partition Function ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Thermodynamic Description ◽  
Black Hole Entropy ◽  
Fundamental Particle ◽  
Horizon Radius

The existence of a thermodynamic description of horizons indicates that space–time has a microstructure. While the "fundamental" degrees of freedom remain elusive, quantizing Einstein's gravity provides some clues about their properties. A quantum AdS black hole possesses an equispaced mass spectrum, independent of Newton's constant, G, when its horizon radius is large compared to the AdS length. Moreover, the black hole's thermodynamics in this limit is inextricably connected with its thermodynamics in the opposite (Schwarzschild) limit by a duality of the Bose partition function. G, absent in the mass spectrum, re-emerges in the thermodynamic description through the Schwarzschild limit, which should be viewed as a natural "ground state." It seems that the Hawking–Page phase transition separates fundamental, "particle-like" degrees of freedom from effective, "geometric" ones.

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 FROM BRICKS TO QUASINORMAL MODES: A NEW PERSPECTIVE ON BLACK HOLE ENTROPY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342027 ◽  
Author(s):  
MICHELE ARZANO ◽  
STEFANO BIANCO ◽  
OLAF DREYER
Keyword(s):  
Black Hole ◽  
Short Distance ◽  
Degrees Of Freedom ◽  
Quasinormal Modes ◽  
Black Hole Entropy ◽  
Quantum Field ◽  
Extended Region ◽  
New Perspective ◽  
The Right ◽  
Dynamical Degrees

Calculations of black hole entropy based on the counting of modes of a quantum field propagating in a Schwarzschild background need to be regularized in the vicinity of the horizon. To obtain the Bekenstein–Hawking result, the short distance cut-off needs to be fixed by hand. In this note, we give an argument for obtaining this cut-off in a natural fashion. We do this by modeling the black hole by its set of quasinormal modes (QNMs). The horizon then becomes a extended region: the quantum ergosphere. The interaction of the quantum ergosphere and the quantum field provides a natural regularization mechanism. The width of the quantum ergosphere provides the right cut-off for the entropy calculation. We arrive at a dual picture of black hole entropy. The entropy of the black hole is given both by the entropy of the quantum field in the bulk and the dynamical degrees of freedom on the horizon.

scholarly journals Goldstone origin of black hole hair from supertranslations and criticality

2016 ◽  
Vol 31 (39) ◽  
pp. 1630045 ◽  
Author(s):  
Artem Averin ◽  
Gia Dvali ◽  
Cesar Gomez ◽  
Dieter Lüst
Keyword(s):  
Black Hole ◽  
Quantum Theory ◽  
Degrees Of Freedom ◽  
Black Hole Entropy ◽  
Vacuum Expectation ◽  
Critical System ◽  
Goldstone Bosons ◽  
Hole Area ◽  
Goldstone Modes ◽  
Geometric Picture

Degrees of freedom that carry black hole entropy and hair can be described in the language of Goldstone phenomenon. They represent the pseudo-Goldstone bosons of certain supertranslations, called [Formula: see text]-transformations, that are spontaneously broken by the black hole metric. This breaking gives rise to a tower of Goldstone bosons created by the spontaneously-broken generators that can be labeled by spherical harmonics. Classically, the number of charges is infinite, they have vanishing vacuum expectation values (VEVs) and the corresponding Goldstone modes are gapless. The resulting hair and entropy are infinite, but unresolvable. In quantum theory, the two things happen. The number of legitimate Goldstone modes restricted by requirement of weak-coupling, becomes finite and scales as black hole area in Planck units. The Goldstones generate a tiny gap, controlled by their gravitational coupling. The gap turns out to be equal to the inverse of black hole half-life, [Formula: see text]. Correspondingly, in quantum theory the charges are neither conserved nor vanish, but non-conservation time is set by [Formula: see text]. This picture nicely matches with the idea of a black hole as critical system is composed of many soft gravitons. The [Formula: see text]-Goldstones of geometric picture represent the near-gapless Bogoliubov–Goldstone modes of critical soft-graviton system.

scholarly journals Is entanglement entropy proportional to area?

2006 ◽  
Vol 84 (6-7) ◽  
pp. 493-499 ◽  
Author(s):  
Morteza Ahmadi ◽  
Saurya Das ◽  
S Shankaranarayanan
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Excited States ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Horizon Area ◽  
03.65 Ud

It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius [Formula: see text], is proportional to the area of the sphere (and not its volume). This suggests that the origin of black-hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.PACS Nos.: 04.60.–m, 04.62, 04.70.–s, 03.65.Ud

scholarly journals Area Entropy and Quantized Mass of Black Holes from Information Theory

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 858
Author(s):  
Dongshan He ◽  
Qingyu Cai
Keyword(s):  
Information Theory ◽  
Black Hole ◽  
Black Hole Entropy ◽  
Quantum Corrections ◽  
Compton Wavelength ◽  
Information Theoretic ◽  
Curved Space ◽  
Thermodynamic Entropy ◽  
Hole Area ◽  
The Relationship

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy.

scholarly journals ENTROPY AND AREA IN LOOP QUANTUM GRAVITY

2005 ◽  
Vol 14 (12) ◽  
pp. 2301-2305
Author(s):  
JOHN SWAIN
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Maximum Entropy ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Black Hole Entropy ◽  
Black Hole Thermodynamics ◽  
Three Dimensions ◽  
Spin Network

Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. We argue that this follows naturally from loop quantum gravity and a result of Kolmogorov and Bardzin' on the the realizability of networks in three dimensions. This represents an alternative to other approaches in which some sort of correlation between field configurations helps limit the degrees of freedom within a region. It also provides an approach to thinking about black hole entropy in terms of states inside rather than on its surface. Intuitively, a spin network complicated enough to imbue a region with volume only lets that volume grow as quickly as the area bounding it.

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 A NEW APPROACH TO BLACK HOLE MICROSTATES

1998 ◽  
Vol 13 (23) ◽  
pp. 1875-1879 ◽  
Author(s):  
RICHARD J. EPP ◽  
R. B. MANN
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Black Hole Entropy ◽  
Space Time ◽  
Orthonormal Frame ◽  
Great Promise ◽  
Frame Field ◽  
New Approach ◽  
Four Dimensions ◽  
First Order

If one encodes the gravitational degrees of freedom in an orthonormal frame field, there is a very natural first-order action one can write down (which in four dimensions is known as the Goldberg action). In this letter we will show that this action contains a boundary action for certain microscopic degrees of freedom living at the horizon of a black hole, and argue that these degrees of freedom hold great promise for explaining the microstates responsible for black hole entropy, in any number of space–time dimensions. This approach faces many interesting challenges, both technical and conceptual.

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