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Statistical description of the black hole degeneracy spectrum
General Relativity and Quantum Cosmology · Submitted 19 Jan 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. | method 0.65 | 0.89 | 0.04 | asserted 0.95 |
| s1 | In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. | contribution 0.98 | 0.43 | 0.05 | unclear 0.54 |
| s2 | We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. | result 1.00 | 0.86 | 0.85 | asserted 1.00 |
| s3 | The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity. | future work 0.68 | 0.33 | 0.05 | hedged possibility 0.65 |
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The paper
Original abstract
We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity.
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How the literature uses it
6 arXiv papers cite this in 13 sentences
Papers citing it · 11 sentences without a confident label
Cites it as background 2 papers
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The relevant counting of microscopic states in the LQG framework is also understood in great detail [ref] .
The thermodynamic limit and black hole entropy in the area ensemble · Introduction · 0.83
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The degeneracy spectrum of black holes and its relation to the entropy has also recently been studied in [ref] .
A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies · Introduction · 0.93
What it cites · 23 sentences without a confident label
Builds on 1 paper
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We end the paper in Section [ref] with our conclusions and some details relevant for the extension of our methods to the $SU(2)$ formulation of [ref] .
Black hole entropy and SU(2) Chern-Simons theory · Introduction · 0.88
Uses the method or tool of 1 paper
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We want to mention here that we restrict our analysis in the main body of the paper to the prescription given by Domagala and Lewandowski in [ref] to compute the entropy.
Black hole entropy from Quantum Geometry · Introduction · 0.89
Compares with 5 papers
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In fact, in the case where the projection constraint is neglected, we easily find [equation] This value must be compared with the one obtained by Meissner in [ref] [equation] Notice that $γ_stairs$ has nothing to do with the value of the Immirzi parameter $πγ_flux=log3$ derived in the context of LQG from the evenly spaced flux area operator used in [ref] which can be interpreted in terms of the Schwarzschild quasinormal modes [ref] .
Black hole entropy in Loop Quantum Gravity · Using the mean: The staircase approximation for the entropy · 0.98
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In fact, in the case where the projection constraint is neglected, we easily find [equation] This value must be compared with the one obtained by Meissner in [ref] [equation] Notice that $γ_stairs$ has nothing to do with the value of the Immirzi parameter $πγ_flux=log3$ derived in the context of LQG from the evenly spaced flux area operator used in [ref] which can be interpreted in terms of the Schwarzschild quasinormal modes [ref] .
Flux-area operator and black hole entropy · Using the mean: The staircase approximation for the entropy · 0.98
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In fact, in the case where the projection constraint is neglected, we easily find [equation] This value must be compared with the one obtained by Meissner in [ref] [equation] Notice that $γ_stairs$ has nothing to do with the value of the Immirzi parameter $πγ_flux=log3$ derived in the context of LQG from the evenly spaced flux area operator used in [ref] which can be interpreted in terms of the Schwarzschild quasinormal modes [ref] .
Quasinormal Modes, the Area Spectrum, and Black Hole Entropy · Using the mean: The staircase approximation for the entropy · 0.98
Cites as background 7 papers
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The modeling of black holes by using space-times admitting isolated horizons as inner boundaries, and the subsequent quantization of this sector of general relativity, has been extensively explained in the literature [ref] .
Quantum Geometry of Isolated Horizons and Black Hole Entropy · Introduction · 1.00
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The modeling of black holes by using space-times admitting isolated horizons as inner boundaries, and the subsequent quantization of this sector of general relativity, has been extensively explained in the literature [ref] .
Black hole entropy and SU(2) Chern-Simons theory · Introduction · 1.00
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The modeling of black holes by using space-times admitting isolated horizons as inner boundaries, and the subsequent quantization of this sector of general relativity, has been extensively explained in the literature [ref] .
Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons · Introduction · 1.00
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