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Black hole horizons from within loop quantum gravity
General Relativity and Quantum Cosmology · Submitted 25 Apr 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom.
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The abstract, sentence by sentence
In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. Similarly, in quantum gravity, the quantized horizon degrees of freedom should result from restricting, or pulling-back, the quantized bulk degrees of freedom. This is not yet fully realized in the - otherwise very successful - quantization of isolated horizons in loop quantum gravity. In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. There is no need to quantize them separately. We present evidence that for a horizon of sphere topology, the resulting horizon theory is remarkably similar to what has been found before.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. | background 1.00 | 0.03 | 0.03 | asserted 1.00 |
| s1 | Similarly, in quantum gravity, the quantized horizon degrees of freedom should result from restricting, or pulling-back, the quantized bulk degrees of freedom. | background 0.97 | 0.06 | 0.08 | hedged possibility 0.59 |
| s2 | This is not yet fully realized in the - otherwise very successful - quantization of isolated horizons in loop quantum gravity. | gap 0.99 | 0.07 | 0.04 | asserted 0.98 |
| s3 | In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. | contribution 0.98 | 0.86 | 0.74 | asserted 0.84 |
| s4 | There is no need to quantize them separately. | interpretation 0.58 | 0.36 | 0.19 | asserted 1.00 |
| s5 | We present evidence that for a horizon of sphere topology, the resulting horizon theory is remarkably similar to what has been found before. | result 0.99 | 0.82 | 0.25 | asserted 0.78 |
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The paper
Original abstract
In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. Similarly, in quantum gravity, the quantized horizon degrees of freedom should result from restricting, or pulling-back, the quantized bulk degrees of freedom. This is not yet fully realized in the - otherwise very successful - quantization of isolated horizons in loop quantum gravity. In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. There is no need to quantize them separately. We present evidence that for a horizon of sphere topology, the resulting horizon theory is remarkably similar to what has been found before.
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References
How the literature uses it
22 arXiv papers cite this in 48 sentences
Papers citing it · 40 sentences without a confident label
Uses its method or tool 1 paper
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If we now trace over the degrees of freedom $|j,m⟩_I$ inside the horizon and use the (quantum) boundary eom [ref] (by computing the scalar product on the internal states $I$ by means of the modified measure defined in [ref] ), the quantum statistical state is given by the density matrix KMS ρ̂=1/Z⊗_p=1^N P^j_p_O e^ı2π/k L̂_p P^j_p_O= 1/Z⊗_p=1^N P^j_p_O e^ı(2π/k-2π) L̂_p P^j_p_O , where the projector $P^j_p_O$ is given by proj P^j_p_O=∑_m_p=-j_p^+j_p|j_p,m_p⟩_O _O⟨j_p,m_p| , and Z Z= (⊗_p=1^N P^j_p_O e^ı(2π/k-2π) L̂_p P^j_p_O) is a normalization factor such that $(ρ̂)=1$.
Geometric temperature and entropy of quantum isolated horizons · KMS-condition · 0.88
Compares with it 2 papers
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We note that the resulting horizon theory seems to reproduce many of the results that have been obtained earlier [ref] , up to the fact that our results point to the theory being ISU(2) instead of SU(2) CS theory, i.e., Euclidean 3d gravity [ref] , due to the fact that on $H$ there remains one nontrivial holonomy and one flux operator per nontrivial cycle of $H$.
Chern-Simons expectation values and quantum horizons from LQG and the Duflo map · Applications · 0.99
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Therefore, the approach taken in [ref] differs from the one adopted in [ref] , since there the boundary and bulk degrees of freedom are no longer treated separately at the quantum level.
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity · Conclusions · 0.94
Cites it as support 1 paper
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As shown in [ref] , holonomies on all contractible loops over the horizon are fixed and there are no local gauge invariant d.o.f. associated to them, in accordance with the expected topological nature of the boundary theory.
Geometric temperature and entropy of quantum isolated horizons · $C^*-$algebra · 0.97
Cites it as background 2 papers
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=1 In last few years, there has been a resurgent interest in the $SU(2)$ gauge theoretic description of Isolated Horizons within LQG framework [ref] .
Entropy of Quantum Black Holes · Recent developments · 0.94
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Although very interesting developments [ref] have been recently carried out towards the characterization of black holes within the full quantum theory, we will follow here the well established, but somehow effective, approach based on starting from a classical space-time containing a black hole.
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity · Quantization · 0.93
What it cites · 34 sentences without a confident label
Uses the method or tool of 1 paper
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The authors of [ref] pointed out a way to resolve this ordering ambiguity by using a device from the theory of Lie algebras, the Duflo map.
Chern-Simons theory, Stokes' Theorem, and the Duflo map · Heuristic considerations · 0.97
Compares with 4 papers
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In the U(1) case, we recover almost verbatim the structure of the quantized horizon of [ref] .
Quantum Geometry of Isolated Horizons and Black Hole Entropy · Discussion and outlook · 1.00
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In the U(1) case, we recover almost verbatim the structure of the quantized horizon of [ref] .
Quantum Geometry and Black Hole Entropy · Discussion and outlook · 1.00
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In the SU(2) case, our results are not complete, but what we saw points towards a very similar picture as [ref] .
Black hole entropy and SU(2) Chern-Simons theory · Discussion and outlook · 0.99
Cites as support 1 paper
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They must be, to a certain extent, distinguishable to account for a linear area-entropy relation [ref] .
Black hole entropy from Quantum Geometry · Gauge invariant solutions · 0.96
Cites as background 15 papers
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The quantization of an isolated horizon is a remarkable success of [ref] .
Black Hole Entropy from Loop Quantum Gravity · Introduction · 0.93
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The quantization of an isolated horizon is a remarkable success of [ref] .
Quantum Black Hole Entropy · Introduction · 0.93
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The quantization of an isolated horizon is a remarkable success of [ref] .
Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons · Introduction · 0.93
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