Entropy

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1467 KiB

Open AccessArticle

Thermodynamic Geometry and Topological Einstein–Yang–Mills Black Holes

by Stefano Bellucci and Bhupendra Nath Tiwari

Entropy 2012, 14(6), 1045-1078; https://doi.org/10.3390/e14061045 - 13 Jun 2012

Cited by 15 | Viewed by 6650

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 [...] Read more.

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)

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311 KiB

Open AccessArticle

Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior

by Irina Dymnikova and Michał Korpusik

Entropy 2011, 13(12), 1967-1991; https://doi.org/10.3390/e13121967 - 28 Nov 2011

Cited by 47 | Viewed by 7271

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 [...] Read more.

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: 8πGT_μ^ν = Λδ_μ^ν as r → 0, 8πGT_μ^ν = λδ_μ^ν 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 M_cr1 ≤ M ≤ M_cr2 it describes a regular cosmological black hole. Space-time in this case has three horizons: a cosmological horizon rc, a black hole horizon r_b < r_c, and an internal horizon r_a < r_b, 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 r_b and cosmological horizon r_c. 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 (r_a = r_b) remnant with the positive specific heat and zero temperature. Full article

(This article belongs to the Special Issue Black Hole Thermodynamics)

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301 KiB

Open AccessArticle

Universal Property of Quantum Gravity implied by Uniqueness Theorem of Bekenstein-Hawking Entropy

by Hiromi Saida

Entropy 2011, 13(9), 1611-1647; https://doi.org/10.3390/e13091611 - 5 Sep 2011

Cited by 11 | Viewed by 6966

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 [...] Read more.

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)

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190 KiB

Open AccessArticle

Effective Conformal Descriptions of Black Hole Entropy

by Steven Carlip

Entropy 2011, 13(7), 1355-1379; https://doi.org/10.3390/e13071355 - 20 Jul 2011

Cited by 47 | Viewed by 6865

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 [...] Read more.

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)

221 KiB

Open AccessArticle

Partition Function of the Schwarzschild Black Hole

by Jarmo Mäkelä

Entropy 2011, 13(7), 1324-1354; https://doi.org/10.3390/e13071324 - 19 Jul 2011

Cited by 14 | Viewed by 6898

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 [...] Read more.

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)

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155 KiB

Open AccessArticle

State Operator Correspondence and Entanglement in AdS₂/CFT₁

by Ashoke Sen

Entropy 2011, 13(7), 1305-1323; https://doi.org/10.3390/e13071305 - 19 Jul 2011

Cited by 88 | Viewed by 7995

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 [...] Read more.

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)

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91 KiB

Open AccessArticle

Is Gravity an Entropic Force?

by Shan Gao

Entropy 2011, 13(5), 936-948; https://doi.org/10.3390/e13050936 - 28 Apr 2011

Cited by 34 | Viewed by 11813

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 [...] Read more.

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)

297 KiB

Open AccessArticle

Static Isolated Horizons: SU(2) Invariant Phase Space, Quantization, and Black Hole Entropy

by Alejandro Perez and Daniele Pranzetti

Entropy 2011, 13(4), 744-777; https://doi.org/10.3390/e13040744 - 25 Mar 2011

Cited by 40 | Viewed by 8770

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 a_H 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 = a_H/(4l ²_p)) 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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