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Metrics with distributional curvature

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David Garfinkle

General Relativity and Quantum Cosmology · Submitted 15 Jun 1999

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

The authors' main claim Here, we generalize their definition to form a wider class: semi-regular metrics.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/9906053 (version 6)
Pith IDRWOVLJFC, Pith's permanent record of this paper and its review
CitationDavid Garfinkle. "Metrics with distributional curvature." arXiv:gr-qc/9906053 (1999). https://pith.science/paper/RWOVLJFC
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,496 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v6. Results and the main claim are underlined; .

This paper considers metrics whose curvature tensor makes sense as a distribution. A class of such metrics, the regular metrics, was defined and studied by Geroch and Traschen. Here, we generalize their definition to form a wider class: semi-regular metrics. We then examine in detail two metrics that are semi-regular but not regular: (i) Minkowski spacetime minus a wedge and (ii) a certain traveling wave metric.

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 This paper considers metrics whose curvature tensor makes sense as a distribution. background 0.66 0.22 0.07 asserted 0.93
s1 A class of such metrics, the regular metrics, was defined and studied by Geroch and Traschen. background 1.00 0.03 0.03 asserted 1.00
s2 Here, we generalize their definition to form a wider class: semi-regular metrics. contribution 1.00 0.92 0.18 asserted 1.00
s3 We then examine in detail two metrics that are semi-regular but not regular: (i) Minkowski spacetime minus a wedge and (ii) a certain traveling wave metric. contribution 0.98 0.91 0.15 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v6
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

This paper considers metrics whose curvature tensor makes sense as a distribution. A class of such metrics, the regular metrics, was defined and studied by Geroch and Traschen. Here, we generalize their definition to form a wider class: semi-regular metrics. We then examine in detail two metrics that are semi-regular but not regular: (i) Minkowski spacetime minus a wedge and (ii) a certain traveling wave metric.

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References
How the literature uses it

3 arXiv papers cite this in 3 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 · 2 sentences without a confident label

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