Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

Asin, Olivier; Achour, Jibril Ben; Geiller, Marc; Noui, Karim; Pérez, Alejandro

doi:10.1103/physrevd.91.084005

Cited by 18 publications

(20 citation statements)

References 34 publications

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“…A physical interpretation of such a result is still missing. Note however that the same value of the chemical potential is also found to cancel the too large quantum correction for the real black hole (γ ∈ R) with the Maxwell Boltzman statistic [16]. Therefore, this behaviour of the quantum correction S cor ∝ √ a H is not specific to the complex model.…”

Section: Semi-classical Limit: Area Law and Logarithmic Correctionsmentioning

confidence: 81%

Analytical continuation of black hole entropy in Loop Quantum Gravity: Lessons from black hole thermodynamics

Achour¹,

Noui²

2016

Proceedings of Frontiers of Fundamental Physics 14 — PoS(FFP14)

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This contribution is devoted to summarize the recent results obtained in the construction of an "analytic continuation" of Loop Quantum Gravity (LQG). By this we mean that we construct analytic continuation of physical quantities in LQG from real values of the Barbero-Immirzi parameter γ to the purely imaginary γ = ±i. This should allow us to define a quantization of gravity with self dual Ashtekar variables. We first realized in [1] that this procedure, when applied to compute the entropy of a spherical black hole in LQG for γ = ±i, allows to reproduce exactly the Bekenstein Hawking area law at the semi classical limit. The rigorous construction of the analytic continuation of spherical black hole entropy has been done in [2]. Here we start with a review of the main steps of this construction: we recall that our prescription turns out to be unique (under natural assumptions) and leads to the right semi-classical limit with its logarithmic quantum corrections. Futhermore, the discrete and γ-dependent area spectrum of the black hole horizon becomes continuous and obviously γ-independent. Then, we review how this analytic continuation could be interpreted in terms of the analytic continuation from the compact gauge group SU(2) to the non compact gauge group SU(1, 1) relying on an analysis of three dimensional quantum gravity.

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Section: Semi-classical Limit: Area Law and Logarithmic Correctionsmentioning

confidence: 81%

Analytical continuation of black hole entropy in Loop Quantum Gravity: Lessons from black hole thermodynamics

Achour¹,

Noui²

2016

Proceedings of Frontiers of Fundamental Physics 14 — PoS(FFP14)

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“…It enters explicitly the spinfoam path integral amplitudes (through the simplicity constraints) [17] while it has been argued to drop out of the symplectic structure after a careful analysis of the LQG discretization scheme [30]. Finally, most predictions from LQG or effective loop gravity models are all γ-dependent, best illustrated by the maximal density of the bouncing universe in Loop Quantum Cosmology (LQC) [31][32][33] or the entropy of isolated horizon [34] and the resulting black hole thermodynamics [35].…”

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confidence: 99%

Thiemann complexifier in classical and quantum FLRW cosmology

Achour

Livine

2017

Phys. Rev. D

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In the context of Loop Quantum Gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic FRW cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates the canonical transformations shifting the Barbero-Immirzi parameter. We focus on the closed algebra consisting in the complexifier, the 3d volume and the Hamiltonian constraint, which we call the CVH algebra. In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a su(1, 1) Lie algebra, with the Hamiltonian as a null generator, the complexifier as a boost and the su(1, 1) Casimir given by the matter density. The loop gravity cosmology approach introduces a regularization length scale λ and regularizes the gravitational Hamiltonian in terms of SU (2) holonomies. We show that this regularization is compatible with the CVH algebra, if we suitably regularize the complexifier and inverse volume factor. The regularized complexifier generates a generalized version of the Barbero's canonical transformation which reduces to the classical one when λ → 0. This structure allows for the exact integration of the actions of the Hamiltonian constraints and the complexifier. This straightforwardly extends to the quantum level: the cosmological evolution is described in terms of SU(1, 1) coherent states and the regularized complexifier generates unitary transformations. The Barbero-Immirzi parameter is to be distinguished from the regularization scale λ, it can be rescaled unitarily and the Immirzi ambiguity ultimately disappears from the physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale transformations. Contents

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“…The fine tuning of the Barbero-Immirzi parameter in the spherically symmetric case led to an alternative model for the entropy state counting[35][36][37]. Based on this model, the dependecy on this parameter of the leading term is shifted to the sub-leading terms for the spherically symmetric horizon.…”

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confidence: 99%

Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Achour¹,

Brahma

2018

Phys. Rev. D

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When applying the techniques of Loop Quantum Gravity (LQG) to symmetry-reduced gravitational systems, one first regularizes the scalar constraint using holonomy corrections, prior to quantization. In inhomogeneous system, where a residual spatial diffeomorphism symmetry survives, such modification of the gauge generator generating time reparametrization can potentially lead to deformations or anomalies in the modified algebra of first class constraints. When working with self-dual variables, it has already been shown that, for spherically symmetric geometry coupled to a scalar field, the holonomy-modified constraints do not generate any modifications to general covariance, as one faces in the real variables formulation, and can thus accommodate local degrees of freedom in such inhomogeneous models. In this paper, we extend this result to Gowdy cosmologies in the self-dual Ashtekar formulation. Furthermore, we show that the introduction of aμ−scheme in midisuperspace models, as is required in the 'improved dynamics' of LQG, is possible in the self-dual formalism while being out of reach in the current effective models suing real-valued Ashtekar-Barbero variables.Our results indicate the advantages of using the self-dual variables to obtain a covariant loop regularization prior to quantization in inhomogeneous symmetry reduced polymer models, implementing additionally the crucialμ-scheme, and thus a consistent semiclassical limit. 2

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Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

Cited by 18 publications

References 34 publications

Analytical continuation of black hole entropy in Loop Quantum Gravity: Lessons from black hole thermodynamics

Analytical continuation of black hole entropy in Loop Quantum Gravity: Lessons from black hole thermodynamics

Thiemann complexifier in classical and quantum FLRW cosmology

Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

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