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Toroidal Perturbations of Friedmann-Robertson-Walker Universes

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Jiri Bicak, Donald Lynden-Bell, Joseph Katz

General Relativity and Quantum Cosmology · Submitted 26 Sep 2003

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

The authors' main claim Explicit expressions are found for the axisymmetric metric perturbations of the closed, flat and open FRW universes caused by toroidal motions of the cosmic fluid.

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arXiv IDgr-qc/0309127 (version 1)
Pith IDKDDHFW2C, Pith's permanent record of this paper and its review
CitationDonald Lynden-Bell, Jiri Bicak, Joseph Katz. "Toroidal Perturbations of Friedmann-Robertson-Walker Universes." arXiv:gr-qc/0309127 (2003). https://pith.science/paper/KDDHFW2C
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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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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,583 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.79 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Explicit expressions are found for the axisymmetric metric perturbations of the closed, flat and open FRW universes caused by toroidal motions of the cosmic fluid. The perturbations are decomposed in vector spherical harmonics on 2-spheres, but the radial dependence is left general. Solutions for general odd-parity $l$-pole perturbations are given for either angular velocities or angular momenta prescribed. In particular, in case of closed universes the solutions require a special treatment of the Legendre equation.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Explicit expressions are found for the axisymmetric metric perturbations of the closed, flat and open FRW universes caused by toroidal motions of the cosmic fluid. result 0.69 0.94 0.65 asserted 1.00
s1 The perturbations are decomposed in vector spherical harmonics on 2-spheres, but the radial dependence is left general. method 0.92 0.89 0.07 asserted 1.00
s2 Solutions for general odd-parity $l$-pole perturbations are given for either angular velocities or angular momenta prescribed. result 0.65 0.91 0.31 asserted 1.00
s3 In particular, in case of closed universes the solutions require a special treatment of the Legendre equation. result 0.35 0.76 0.07 asserted 1.00

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

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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

Explicit expressions are found for the axisymmetric metric perturbations of the closed, flat and open FRW universes caused by toroidal motions of the cosmic fluid. The perturbations are decomposed in vector spherical harmonics on 2-spheres, but the radial dependence is left general. Solutions for general odd-parity $l$-pole perturbations are given for either angular velocities or angular momenta prescribed. In particular, in case of closed universes the solutions require a special treatment of the Legendre equation.

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