RECORD
A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies
General Relativity and Quantum Cosmology · Submitted 24 Jan 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In all scenarios, the internal symmetry may be reduced to combinations of U(1).
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
The abstract, sentence by sentence
It is known that the SU(2) degrees of freedom manifest in the description of the gravitational field in loop quantum gravity are generally reduced to U(1) degrees of freedom on an $S^2$ isolated horizon. General relativity also allows black holes with planar, toroidal, or higher genus topology for their horizons. These solutions also meet the criteria for an isolated horizon, save for the topological criterion, which is not crucial. We discuss the relevant corresponding symmetry reduction for black holes of various topologies (genus 0 and $\geq 2$) here and discuss its ramifications to black hole entropy within the loop quantum gravity paradigm. Quantities relevant to the horizon theory are calculated explicitly using a generalized ansatz for the connection and densitized triad, as well as utilizing a general metric admitting hyperbolic sub-spaces. In all scenarios, the internal symmetry may be reduced to combinations of U(1).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is known that the SU(2) degrees of freedom manifest in the description of the gravitational field in loop quantum gravity are generally reduced to U(1) degrees of freedom on an $S^2$ isolated horizon. | background 1.00 | 0.04 | 0.07 | asserted 1.00 |
| s1 | General relativity also allows black holes with planar, toroidal, or higher genus topology for their horizons. | background 0.99 | 0.05 | 0.03 | asserted 0.87 |
| s2 | These solutions also meet the criteria for an isolated horizon, save for the topological criterion, which is not crucial. | background 0.93 | 0.10 | 0.06 | asserted 0.98 |
| s3 | We discuss the relevant corresponding symmetry reduction for black holes of various topologies (genus 0 and $\geq 2$) here and discuss its ramifications to black hole entropy within the loop quantum gravity paradigm. | contribution 1.00 | 0.88 | 0.20 | asserted 0.84 |
| s4 | Quantities relevant to the horizon theory are calculated explicitly using a generalized ansatz for the connection and densitized triad, as well as utilizing a general metric admitting hyperbolic sub-spaces. | method 1.00 | 0.91 | 0.05 | asserted 0.99 |
| s5 | In all scenarios, the internal symmetry may be reduced to combinations of U(1). | result 1.00 | 0.78 | 0.67 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
It is known that the SU(2) degrees of freedom manifest in the description of the gravitational field in loop quantum gravity are generally reduced to U(1) degrees of freedom on an $S^2$ isolated horizon. General relativity also allows black holes with planar, toroidal, or higher genus topology for their horizons. These solutions also meet the criteria for an isolated horizon, save for the topological criterion, which is not crucial. We discuss the relevant corresponding symmetry reduction for black holes of various topologies (genus 0 and $\geq 2$) here and discuss its ramifications to black hole entropy within the loop quantum gravity paradigm. Quantities relevant to the horizon theory are calculated explicitly using a generalized ansatz for the connection and densitized triad, as well as utilizing a general metric admitting hyperbolic sub-spaces. In all scenarios, the internal symmetry may be reduced to combinations of U(1).
Human review
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 1 paper
-
* Horizons with nontrivial topologies and their quantization in have been studied in a very interesting series of articles [ref] .
Black hole horizons from within loop quantum gravity · Discussion and outlook · 0.99
What it cites · 1 sentence without a confident label
Cites as background 3 papers
-
A calculation of the entropy in the SU(2) formalism incorporating quantum group corrections has recently been conducted in [ref] .
The SU(2) Black Hole entropy revisited · Introduction · 0.93
-
However, general relativity admits horizons with other topologies such as planar, toroidal and higher genus topologies [ref] - [ref] .
Gravitational Collapse to Toroidal and Higher Genus asymptotically AdS Black Holes · Introduction · 0.84
-
The degeneracy spectrum of black holes and its relation to the entropy has also recently been studied in [ref] .
Statistical description of the black hole degeneracy spectrum · Introduction · 0.93
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.