Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity

Achour, Jibril Ben; Mouchet, Amaury; Noui, Karim

doi:10.48550/arxiv.1406.6021

Cited by 33 publications

(98 citation statements)

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“…Indeed, these corrections are typically expected to be logarithmic (as functions of a H ), and therefore one should look for a mechanism able to suppress the too large √ a H contributions. It has been shown in [22] that the introduction of a non-vanishing chemical potential allows to eliminate these too large corrections and to replace them by logarithmic ones, at least in the case where the (undistinguishable) punctures satisfy the classical Maxwell-Boltzmann statistics and when the holographic degeneracy is saturated (i.e. δ h = 0).…”

Section: B Setup and Resultsmentioning

confidence: 99%

“…δ h = 0). To understand how this comes about, let us briefly reproduce the main steps of the calculation in [22] when δ h = 0 (for the sake of generality).…”

Section: B Setup and Resultsmentioning

confidence: 99%

“…In summary, one has that in both cases above a fine tuning of the chemical potential can eliminate the too large subleading corrections to the entropy, which in turns leaves room for hypothetical logarithmic corrections. This expectation is realized in [22], where it has been shown that taking into account polynomial corrections to the degeneracy (which come from the asymptotic expansion of the number of black holes microstates in LQG) leads to the appearance of logarithmic corrections.…”

Section: Holography and Entropymentioning

confidence: 96%

“…It is this expression for the degeneracy (with P ( n j ) = 1) which was taken in [12] as the starting point for the study of the statistical mechanics of the quantum black holes in various thermodynamical ensembles. In a series of papers [20][21][22], it was shown that an analytic continuation of the Barbero-Immirzi parameter to γ = ±i leads to a holographic behavior for (2.5).…”

Section: A Degeneracy Of the Microstatesmentioning

confidence: 99%

“…In that case, the semi-classical limit is obtained only when δ β → 0, which means that β approaches the inverse Unruh temperature. This was studied in [22], where it was shown that the asymptotic expansion of the entropy takes the form…”

Section: Holography and Entropymentioning

confidence: 99%

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

et al. 2015

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We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop quantum gravity, the black hole microstates are defined by finite families of half-integers spins coloring the punctures, and the near-horizon energy measured by quasi-local stationary observers defines the various thermodynamical ensembles. The punctures carry excitations of quantum geometry in the form of quanta of area, and the total horizon area a H is given by the sum of these microscopic contributions. We assume here that the system satisfies the Bose-Einstein statistics, and that each microstate is degenerate with a holographic degeneracy given by exp λa H /ℓ 2 Pl and λ > 0. We analyze in detail the thermodynamical properties resulting from these inputs, and in particular compute the grand canonical entropy. We explain why the requirements that the temperature be fixed to the Unruh temperature and that the chemical potential vanishes do not specify completely the semi-classical regime of large horizon area, and classify in turn what the various regimes can be. When the degeneracy saturates the holographic bound (λ = 1/4), there exists a semi-classical regime in which the subleading corrections to the entropy are logarithmic. Furthermore, this regime corresponds to a Bose-Einstein condensation, in the sense that it is dominated by punctures carrying the minimal (or ground state) spin value 1/2.

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Section: B Setup and Resultsmentioning

confidence: 99%

“…δ h = 0). To understand how this comes about, let us briefly reproduce the main steps of the calculation in [22] when δ h = 0 (for the sake of generality).…”

Section: B Setup and Resultsmentioning

confidence: 99%

Section: Holography and Entropymentioning

confidence: 96%

Section: A Degeneracy Of the Microstatesmentioning

confidence: 99%

Section: Holography and Entropymentioning

confidence: 99%

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

et al. 2015

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Analytic continuation of the rotating black hole state counting

Achour

Noui

Pérez

2016

J. High Energ. Phys.

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Super Cartan Geometry and the Super Ashtekar Connection

Eder

2023

Ann. Henri Poincaré

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This work is devoted to the geometric approach to supergravity. More precisely, we interpret $$\mathcal {N}=1$$ N = 1 , $$D=4$$ D = 4 supergravity as a super Cartan geometry which provides a link between supergravity and Yang–Mills theory. To this end, we first review important aspects of the theory of supermanifolds and we establish a link between various different approaches. We then introduce super Cartan geometries using the concept of so-called enriched categories. This, among other things, will enable us to implement anticommutative fermionic fields. We will then also show that non-extended $$D=4$$ D = 4 supergravity naturally arises in this framework. Finally, using this gauge-theoretic interpretation as well as the chiral structure of the underlying supersymmetry algebra, we will derive graded analoga of Ashtekar’s self-dual variables and interpret them in terms of generalized super Cartan connections. This gives canonical chiral supergravity the structure of a Yang–Mills theory with gauge supergroup similar to the self-dual variables in ordinary first-order Einstein gravity. We then construct the parallel transport map corresponding to the super connection in mathematical rigorous way using again enriched categories. This provides the possibility of quantizing gravity and matter degrees of freedom in loop quantum gravity in a unified way. Kindly check and confirm inserted city and country name are correctly identified.City and country name are correct.

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Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity

Cited by 33 publications

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

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

Analytic continuation of the rotating black hole state counting

Super Cartan Geometry and the Super Ashtekar Connection

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