Black hole entropy from loop quantum gravity in higher dimensions

Norbert Bodendorfer

RECORD

Black hole entropy from loop quantum gravity in higher dimensions

Norbert Bodendorfer

General Relativity and Quantum Cosmology · Submitted 18 Jul 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The state counting problem effectively reduces to the well studied 3+1-dimensional one based on an SU(2)-Chern-Simons theory, differing only in the precise form of the area spectrum.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,296 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.28 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We propose a derivation for computing black hole entropy for spherical non-rotating isolated horizons from loop quantum gravity in four and higher dimensions. The state counting problem effectively reduces to the well studied 3+1-dimensional one based on an SU(2)-Chern-Simons theory, differing only in the precise form of the area spectrum.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose a derivation for computing black hole entropy for spherical non-rotating isolated horizons from loop quantum gravity in four and higher dimensions.	contribution 1.00	0.88	0.38	asserted 0.73
s1	The state counting problem effectively reduces to the well studied 3+1-dimensional one based on an SU(2)-Chern-Simons theory, differing only in the precise form of the area spectrum.	method 0.92	0.60	0.22	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We propose a derivation for computing black hole entropy for spherical non-rotating isolated horizons from loop quantum gravity in four and higher dimensions. The state counting problem effectively reduces to the well studied 3+1-dimensional one based on an SU(2)-Chern-Simons theory, differing only in the precise form of the area spectrum.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Edge modes of gravity. Part III. Corner simplicity constraints
hep-th 2020-07 conditional novelty 7.0 of 10

The corner area element equals the Poincaré spin Casimir, and the continuum simplicity constraints split into two second class and one first class component, leaving the full Lorentz algebra as Dirac observables.
Edge modes of gravity -- II: Corner metric and Lorentz charges
hep-th 2020-07 conditional novelty 6.0 of 10

The corner metric of tetrad gravity satisfies an ultra-local sl(2,R) algebra whose Casimir is the corner area element, and its space-like nature places that Casimir in the unitary discrete series, giving a quantized a...
Edge modes of gravity -- I: Corner potentials and charges
hep-th 2020-06 conditional novelty 5.0 of 10

Different formulations of gravity differ only by corner terms in their symplectic potentials, and those corner terms decide which corner symmetries are non-trivially represented.

How the literature uses it

15 arXiv papers cite this in 38 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 31 sentences without a confident label

Builds on it 1 paper

In higher dimensions and for Lanczos-Lovelock gravity, one can apply the entropy computation of [ref] to the boundary Hilbert space from section [ref] [ref] .

The Wald entropy formula and loop quantum gravity · The large-spin limit and sending $γ$ to $±i$ · 0.88

Cites it as support 1 paper

In deriving the higher-dimensional minimum-length modified QM we were guided by two recent papers [ref] demonstrating (in the framework of string theory and loop quantum gravity) that the logarithmic corrections to the BH entropy is universal in arbitrary space-time dimensions.

Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences · Summary · 0.99

Cites it as background 4 papers

In this subsection, we will briefly introduce the higher-dimensional connection variables, and review the entropy results [ref] that arise from them.

The Wald entropy formula and loop quantum gravity · Entropy in higher-dimensional LQG · 0.86
While this paper doesn't provide (long) technical calculations as e.g. its companions [ref] , it focuses on some conceptual questions left open there which have, to the best of the author's knowledge, not been addressed in a comprehensive fashion elsewhere in the literature.

A note on entanglement entropy and quantum geometry · Introduction · 0.80
They have also been discussed extensively in the context of black hole entropy counting in [ref] .

Corner symmetry and quantum geometry · Charges and discreteness · 0.95

What it cites · 56 sentences without a confident label

Builds on 2 papers

If we still restrict to global gauge invariance on $H$ and apply the arguments of [ref] , the derivation goes through also here.

Black holes in full quantum gravity · Comments · 0.86
Thus, the foundation of the ideas discussed in [ref] extends to higher dimensions.

Polyhedra in loop quantum gravity · Polyhedral viewpoint · 0.99

Uses the method or tool of 7 papers

In this section, we will recall the isolated horizon degrees of freedom using the dimension-independent connection variables as derived in [ref] .

New Variables for Classical and Quantum Gravity in all Dimensions V. Isolated Horizon Boundary Degrees of Freedom · Isolated horizon degrees of freedom · 0.83
In this section, we will recall the isolated horizon degrees of freedom using the dimension-independent connection variables as derived in [ref] .

The Wald entropy formula and loop quantum gravity · Isolated horizon degrees of freedom · 0.83
For this, we choose a maximally commuting subset by imagining the edges puncturing $H$ in each of the two charts to be connected to a spin network vertex and following the recipe in [ref] .

On the Implementation of the Canonical Quantum Simplicity Constraint · Quantization · 0.99

Compares with 6 papers

For $λ= 1$ as the lowest possible representation label, we obtain the logarithmic correction $-3/2 Log(A)$ found by Carlip in any dimension [ref] and thus confirm this calculation from an independent point of view.

Logarithmic Corrections to Black Hole Entropy from the Cardy Formula · Entropy calculation · 0.89
We thus further restrict to constant $Λ_IJ$ on $H$ and note that also in the U$(1)$ framework in $3+1$ dimensions [ref] , the restriction to constant $Λ_IJ$ on $H$ becomes necessary, however for different reasons [ref] .

Isolated Horizons: the Classical Phase Space · Constraint algebra · 0.91
We thus further restrict to constant $Λ_IJ$ on $H$ and note that also in the U$(1)$ framework in $3+1$ dimensions [ref] , the restriction to constant $Λ_IJ$ on $H$ becomes necessary, however for different reasons [ref] .

Quantum Geometry of Isolated Horizons and Black Hole Entropy · Constraint algebra · 0.91

Cites as support 1 paper

They do not form a closing algebra, see e.g. [ref] , and are thus second class in Dirac's terminology [ref] .

New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory · Constraint algebra · 0.97

Cites as background 9 papers

We demand $Δ$ to be a spherical non-rotating isolated horizon, see [ref] for details.

New Variables for Classical and Quantum Gravity in all Dimensions V. Isolated Horizon Boundary Degrees of Freedom · Conditions on $Δ$ · 0.81
Here, the calculation of black hole entropy is translated to the calculation of the entropy of isolated horizons, see [ref] for a review.

Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity · Introduction · 0.91
See [ref] for more discussion on this route.

Loop quantum gravity without the Hamiltonian constraint · Entropy calculation · 0.86

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.