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Special Issue "Black Hole Thermodynamics"

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Astrophysics and Cosmology".

Deadline for manuscript submissions: closed (30 June 2011)

Special Issue Editor

Guest Editor
Prof. Dr. Jacob D. Bekenstein

Polak Professor of Theoretical Physics, Racah Institute of Physics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel
Website | E-Mail
Phone: 972-2-6584374
Fax: +972 (0)2 5611519
Interests: gravitational theory; black hole physics; relativistic magnetohydrodynamics; galactic dynamics; physical aspects of information theory; physics of the vacuum

Special Issue Information

Dear Colleagues,

In the four decades since its introduction into black hole physics, black hole entropy has proved a resilient and wide-ranging notion, with conceptual connections to a number of areas of the physical sciences, some far removed from black hole physics.    Its wide applicability in the gravitational world has become clear as new types of black holes from a variety of gravity theories have been characterized theoretically.  Black hole entropy naturally engendered the generalized second law which has found innumerable applications, from ruling out many conceivable black hole processes or conceivable denizens of the universe, to suggesting entropy bounds of various sorts to restricting the evolution of inflationary cosmological models through a natural extension of concepts.  One bound---the holographic entropy bound---served as motivation for the holographic principle, a rule which has greatly impacted contemporary high energy physics and string theory.  This principle is nowadays touted as a guide to quantum gravity.  In fact, the very form of black hole entropy has often invited exploration, from novel perspectives, of the quantum gravity challenge.  The area law of black hole entropy motivated the study of entanglement entropy in various contexts, and has found counterparts in condensed matter physics.  The rich history of the subject would suggest that we have not seen the end of it.

Prof. Dr. Jacob D. Bekenstein
Guest Editor

Keywords

  • area law
  • microstates
  • quantum corrections
  • black hole thermodynamics
  • generalized second law
  • holographic principle
  • holographic duals
  • AdS/CFT
  • entanglement entropy

Published Papers (8 papers)

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Research

Open AccessArticle Thermodynamic Geometry and Topological Einstein–Yang–Mills Black Holes
Entropy 2012, 14(6), 1045-1078; doi:10.3390/e14061045
Received: 25 April 2012 / Revised: 8 June 2012 / Accepted: 11 June 2012 / Published: 13 June 2012
Cited by 6 | PDF Full-text (1467 KB) | HTML Full-text | XML Full-text
Abstract
From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein–Yang–Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher dimensional
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From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein–Yang–Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher dimensional gravity, we provide the criteria for the local and global statistical stability of an ensemble of topological Einstein–Yang–Mills black holes in arbitrary spacetime dimensions D ≥ 5. Finally, as per the formulations of the thermodynamic geometry, we offer a parametric account of the statistical consequences in both the local and global fluctuation regimes of the topological extremal Einstein–Yang–Mills black holes. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior
Entropy 2011, 13(12), 1967-1991; doi:10.3390/e13121967
Received: 3 August 2011 / Revised: 14 November 2011 / Accepted: 16 November 2011 / Published: 28 November 2011
Cited by 10 | PDF Full-text (311 KB) | HTML Full-text | XML Full-text
Abstract
We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de
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We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant: 8πGTμν = Λδμν as r → 0, 8πGTμν = λδμν as r → ∞ with λ < Λ. It represents an anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. In the range of the mass parameter Mcr1 ≤ M ≤ Mcr2 it describes a regular cosmological black hole. Space-time in this case has three horizons: a cosmological horizon rc, a black hole horizon rb < rc, and an internal horizon ra < rb, which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. We present the basicfeatures of space-time geometry and the detailed analysis of thermodynamics of horizons using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. We find that in a certain range of parameters M and q =√Λ/λ there exist a global temperature for an observer in the R-region between the black hole horizon rb and cosmological horizon rc. We show that a second-order phase transition occurs in the course of evaporation, where a specific heat is broken and a temperature achieves its maximal value. Thermodynamical preference for a final point of evaporation is thermodynamically stable double-horizon (ra = rb) remnant with the positive specific heat and zero temperature. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle Universal Property of Quantum Gravity implied by Uniqueness Theorem of Bekenstein-Hawking Entropy
Entropy 2011, 13(9), 1611-1647; doi:10.3390/e13091611
Received: 22 June 2011 / Revised: 28 August 2011 / Accepted: 31 August 2011 / Published: 5 September 2011
Cited by 5 | PDF Full-text (301 KB)
Abstract
This paper consists of three parts. In the first part, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion. In the second part, intrinsic properties
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This paper consists of three parts. In the first part, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion. In the second part, intrinsic properties of quantum mechanics are shown, which justify the Boltzmann formula to yield a unique entropy in statistical mechanics. These properties clarify three conditions, one of which is necessary and others are sufficient for the validity of Boltzmann formula. In the third part, by combining the above results, we find a reasonable suggestion from the sufficient conditions that the potential of gravitational interaction among microstates of underlying quantum gravity may not diverge to negative infinity (such as Newtonian gravity) but is bounded below at a finite length scale. In addition to that, from the necessary condition, the interaction has to be repulsive within the finite length scale. The length scale should be Planck size. Thus, quantum gravity may become repulsive at Planck length. Also, a relation of these suggestions with action integral of gravity at semi-classical level is given. These suggestions about quantum gravity are universal in the sense that they are independent of any existing model of quantum gravity. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle Effective Conformal Descriptions of Black Hole Entropy
Entropy 2011, 13(7), 1355-1379; doi:10.3390/e13071355
Received: 1 July 2011 / Revised: 12 July 2011 / Accepted: 19 July 2011 / Published: 20 July 2011
Cited by 21 | PDF Full-text (190 KB) | HTML Full-text | XML Full-text
Abstract
It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though, is the universality of these thermodynamic properties: their exceptionally simple and general form, and the fact that they can be derived from many very different descriptions
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It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though, is the universality of these thermodynamic properties: their exceptionally simple and general form, and the fact that they can be derived from many very different descriptions of the underlying microscopic degrees of freedom. I review the proposal that this universality arises from an approximate conformal symmetry, which permits an effective “conformal dual” description that is largely independent of the microscopic details. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle State Operator Correspondence and Entanglement in AdS2/CFT1
Entropy 2011, 13(7), 1305-1323; doi:10.3390/e13071305
Received: 13 June 2011 / Accepted: 22 June 2011 / Published: 19 July 2011
Cited by 47 | PDF Full-text (155 KB) | HTML Full-text | XML Full-text
Abstract
Since Euclidean global AdS2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor
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Since Euclidean global AdS2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor product of two copies of the Hilbert space. Using this picture we argue that the corresponding states in the dual string theory living on AdS2 × K are described by the twisted version of the Hartle–Hawking states, the twists being generated by a large unitary group of symmetries that this string theory must possess. This formalism makes natural the dual interpretation of the black hole entropy—as the logarithm of the degeneracy of ground states of the quantum mechanics describing the low energy dynamics of the black hole, and also as an entanglement entropy between the two copies of the same quantum theory living on the two boundaries of global AdS2 separated by the event horizon. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle Partition Function of the Schwarzschild Black Hole
Entropy 2011, 13(7), 1324-1354; doi:10.3390/e13071324
Received: 23 May 2011 / Revised: 8 July 2011 / Accepted: 13 July 2011 / Published: 19 July 2011
Cited by 4 | PDF Full-text (221 KB) | HTML Full-text | XML Full-text
Abstract
We consider a microscopic model of a stretched horizon of the Schwarzschild black hole. In our model the stretched horizon consists of a finite number of discrete constituents. Assuming that the quantum states of the Schwarzschild black hole are encoded in the quantum
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We consider a microscopic model of a stretched horizon of the Schwarzschild black hole. In our model the stretched horizon consists of a finite number of discrete constituents. Assuming that the quantum states of the Schwarzschild black hole are encoded in the quantum states of the constituents of its stretched horizon in a certain manner we obtain an explicit, analytic expression for the partition function of the hole. Our partition function predicts, among other things, the Hawking effect, and provides it with a microscopic, statistical interpretation. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle Is Gravity an Entropic Force?
Entropy 2011, 13(5), 936-948; doi:10.3390/e13050936
Received: 2 March 2011 / Revised: 7 April 2011 / Accepted: 24 April 2011 / Published: 28 April 2011
Cited by 22 | PDF Full-text (91 KB) | HTML Full-text | XML Full-text
Abstract
The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic
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The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This may provide a further support for the conclusion that gravity is not an entropic force. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)
Open AccessArticle Static Isolated Horizons: SU(2) Invariant Phase Space, Quantization, and Black Hole Entropy
Entropy 2011, 13(4), 744-777; doi:10.3390/e13040744
Received: 22 February 2011 / Revised: 16 March 2011 / Accepted: 16 March 2011 / Published: 25 March 2011
Cited by 22 | PDF Full-text (297 KB) | HTML Full-text | XML Full-text
Abstract
We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2) invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to
[...] Read more.
We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2) invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non-conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance. Restricting our attention to static isolated horizons we study the effective theories describing the boundary degrees of freedom. A quantization of the horizon degrees of freedom is proposed. By defining a statistical mechanical ensemble where only the area aH of the horizon is fixed macroscopically—states with fluctuations away from spherical symmetry are allowed—we show that it is possible to obtain agreement with the Hawkings area law (S = aH /(4l 2p)) without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics)

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