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p. 1045-1078
Received: 25 April 2012 / Revised: 8 June 2012 / Accepted: 11 June 2012 / Published: 13 June 2012

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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 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.

p. 1967-1991
Received: 3 August 2011 / Revised: 14 November 2011 / Accepted: 16 November 2011 / Published: 28 November 2011

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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 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.

p. 1611-1647
Received: 22 June 2011 / Revised: 28 August 2011 / Accepted: 31 August 2011 / Published: 5 September 2011

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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 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.

p. 1355-1379
Received: 1 July 2011 / Revised: 12 July 2011 / Accepted: 19 July 2011 / Published: 20 July 2011

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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 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.

p. 1305-1323
Received: 13 June 2011 / Accepted: 22 June 2011 / Published: 19 July 2011

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Abstract: Since Euclidean global AdS_{2} space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT_{1} 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 AdS_{2} × 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 AdS_{2} separated by the event horizon.

p. 1324-1354
Received: 23 May 2011 / Revised: 8 July 2011 / Accepted: 13 July 2011 / Published: 19 July 2011

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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 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.

p. 936-948
Received: 2 March 2011 / Revised: 7 April 2011 / Accepted: 24 April 2011 / Published: 28 April 2011

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| Cited by 14 | 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 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.

p. 744-777
Received: 22 February 2011 / Revised: 16 March 2011 / Accepted: 16 March 2011 / Published: 25 March 2011

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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 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.

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