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Exact solutions of Einstein and Einstein-scalar equations in 2 + 1 dimensions

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K. S. Virbhadra

General Relativity and Quantum Cosmology · Submitted 29 Aug 1994

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

The authors' main claim A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/9408035 (version 1)
Pith ID4N5BCHHW, Pith's permanent record of this paper and its review
CitationK. S. Virbhadra. "Exact solutions of Einstein and Einstein-scalar equations in 2 + 1 dimensions." arXiv:gr-qc/9408035 (1994). https://pith.science/paper/4N5BCHHW
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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, 4,261 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.75 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For $\Lambda = 0 $, the spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at $r =0$ and the scalar field diverges at $r=0$ as well as at infinity .

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 A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. contribution 0.88 0.95 0.56 asserted 1.00
s1 This is a nonstatic generalization of the uncharged spinless BTZ metric. interpretation 0.66 0.72 0.15 asserted 1.00
s2 For $\Lambda = 0 $, the spacetime is though not flat, the Kretschmann invariant vanishes. result 0.99 0.83 0.08 asserted 1.00
s3 The energy, momentum, and power output for this metric are obtained. result 0.67 0.93 0.12 asserted 1.00
s4 Further a static and circularly symmetric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at $r =0$ and the scalar field diverges at $r=0$ as well as at infinity . contribution 0.86 0.93 0.16 asserted 1.00

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

What was examined, and what was not

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  • 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

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For $\Lambda = 0 $, the spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at $r =0$ and the scalar field diverges at $r=0$ as well as at infinity .

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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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