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General Relativity and Quantum Cosmology · arXiv:gr-qc/9802005 v1 · submitted 3 Feb 1998

Caustics of Compensated Spherical Lens Models

G. F. R. Ellis, D. M. Solomons (UCT)

PDF · arXiv · The abstract, sentence by sentence · Cite

The paper says

“Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.”

from the abstract · picked out as the main claim by a classifier

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The paper

Abstract

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.

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

How the main claim is stated: asserted 0.98

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.84 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. contribution 0.79 0.70 0.06 unclear 0.69
Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect. result 0.93 0.83 0.84 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.86

What was examined, and what was not

Sources read

  • arXiv listing abstract v1

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

How the labels were made

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,340 input tokens, $0.0001 reported.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Cited by 5 Pith papers

Reviewed papers on Pith that cite this one. The full citation record

  1. Geodesic-light-cone coordinates and the Bianchi I spacetime gr-qc · Feb 2016
  2. Average expansion rate and light propagation in a cosmological Tardis spacetime astro-ph.CO · Aug 2013
  3. Is there proof that backreaction of inhomogeneities is irrelevant in cosmology? gr-qc · May 2015
  4. Evaluating backreaction with the peak model of structure formation astro-ph · Jan 2008
  5. Accelerated expansion from structure formation astro-ph · Jul 2006
How the literature uses it

6 arXiv papers cite this in 9 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 · 4 sentences without a confident label

Contests it 2 papers
  • Although this claim and its justification are inaccurate—as already noticed by Bertotti [ref] and emphasized later on by several authors [ref] —a weaker version of it has been formulated by Kibble & Lieu, who showed that in a locally inhomogeneous Universe the total area of a constant-affine-parameter surface is essentially unaffected by gravitational lensing [ref] .

    Geodesic-light-cone coordinates and the Bianchi I spacetime · Directional average of the inverse magnification · contest 0.74

  • However, the proof presented in [ref] assumes that the angular element is given by the FRW metric, which is the question to be investigated [ref] , and the LTB model has been used to provide an exact counterexample [ref] (see also [ref] ).

    Average expansion rate and light propagation in a cosmological Tardis spacetime · Discussion · contest 0.91

Cites it as support 1 paper
Cites it as background 2 papers

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