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Ricci and Matter inheritance collineations of Robertson-Walker space-times

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Pantelis S. Apostolopoulos, Michael Tsamparlis

General Relativity and Quantum Cosmology · Submitted 8 Oct 2001

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

The authors' main claim It is shown that these higher order symmetries can be used as supplementary conditions to produce an equation of state which is compatible with the Geometry and the Physics of the Robertson-Walker space-times.

how it is stated · asserted 0.97 read the record →

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arXiv IDgr-qc/0110042 (version 1)
Pith IDS7MN5QAF, Pith's permanent record of this paper and its review
CitationMichael Tsamparlis, Pantelis S. Apostolopoulos. "Ricci and Matter inheritance collineations of Robertson-Walker space-times." arXiv:gr-qc/0110042 (2001). https://pith.science/paper/S7MN5QAF
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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, 4,993 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

It is well known that every Killing vector is a Ricci and Matter collineation. Therefore the metric, the Ricci tensor and the energy-momentum tensor are all members of a large family of second order symmetric tensors which are invariant under a common group of symmetries. This family is described by a generic metric which is defined from the symmetry group of the space-time metric. The proper Ricci and Matter (inheritance) collineations are the (conformal) Killing vectors of the generic metric which are not (conformal) Killing vectors of the space-time metric. Using this observation we compute the Ricci and Matter inheritance collineations of the Robertson-Walker space-times and we determine the Ricci and Matter collineations without any further calculations. It is shown that these higher order symmetries can be used as supplementary conditions to produce an equation of state which is compatible with the Geometry and the Physics of the Robertson-Walker space-times.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 It is well known that every Killing vector is a Ricci and Matter collineation. background 1.00 0.04 0.04 asserted 1.00
s1 Therefore the metric, the Ricci tensor and the energy-momentum tensor are all members of a large family of second order symmetric tensors which are invariant under a common group of symmetries. background 0.48 0.15 0.08 asserted 1.00
s2 This family is described by a generic metric which is defined from the symmetry group of the space-time metric. method 0.50 0.46 0.06 asserted 1.00
s3 The proper Ricci and Matter (inheritance) collineations are the (conformal) Killing vectors of the generic metric which are not (conformal) Killing vectors of the space-time metric. method 0.58 0.41 0.20 asserted 1.00
s4 Using this observation we compute the Ricci and Matter inheritance collineations of the Robertson-Walker space-times and we determine the Ricci and Matter collineations without any further calculations. contribution 0.63 0.95 0.27 asserted 1.00
s5 It is shown that these higher order symmetries can be used as supplementary conditions to produce an equation of state which is compatible with the Geometry and the Physics of the Robertson-Walker space-times. result 0.75 0.87 0.51 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • 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

It is well known that every Killing vector is a Ricci and Matter collineation. Therefore the metric, the Ricci tensor and the energy-momentum tensor are all members of a large family of second order symmetric tensors which are invariant under a common group of symmetries. This family is described by a generic metric which is defined from the symmetry group of the space-time metric. The proper Ricci and Matter (inheritance) collineations are the (conformal) Killing vectors of the generic metric which are not (conformal) Killing vectors of the space-time metric. Using this observation we compute the Ricci and Matter inheritance collineations of the Robertson-Walker space-times and we determine the Ricci and Matter collineations without any further calculations. It is shown that these higher order symmetries can be used as supplementary conditions to produce an equation of state which is compatible with the Geometry and the Physics of the Robertson-Walker space-times.

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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

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