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On a Peculiar Family of Static, Axisymmetric, Vacuum Solutions of the Einstein Equations
General Relativity and Quantum Cosmology · Submitted 24 Dec 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By computing the area, we establish that the singular region is `point-like'.
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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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The abstract, sentence by sentence
The Zipoy-Voorhees family of static, axisymmetric vacuum solutions forms an interesting family in that it contains the Schwarzschild black hole excepting which all other members have naked singularity. We analyze some properties of the region near singularity by studying a natural family of 2-surfaces. We establish that these have the topology of the 2-sphere by an application of the Gauss-Bonnet theorem. By computing the area, we establish that the singular region is `point-like'. Isometric embedding of these surfaces in the three dimensional Euclidean space is used to distinguish the two types of deviations from spherical symmetry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Zipoy-Voorhees family of static, axisymmetric vacuum solutions forms an interesting family in that it contains the Schwarzschild black hole excepting which all other members have naked singularity. | background 1.00 | 0.07 | 0.10 | asserted 1.00 |
| s1 | We analyze some properties of the region near singularity by studying a natural family of 2-surfaces. | contribution 0.87 | 0.92 | 0.05 | asserted 0.84 |
| s2 | We establish that these have the topology of the 2-sphere by an application of the Gauss-Bonnet theorem. | result 0.86 | 0.94 | 0.14 | asserted 1.00 |
| s3 | By computing the area, we establish that the singular region is `point-like'. | result 0.99 | 0.94 | 0.32 | asserted 1.00 |
| s4 | Isometric embedding of these surfaces in the three dimensional Euclidean space is used to distinguish the two types of deviations from spherical symmetry. | method 0.92 | 0.85 | 0.08 | asserted 0.99 |
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The paper
Original abstract
The Zipoy-Voorhees family of static, axisymmetric vacuum solutions forms an interesting family in that it contains the Schwarzschild black hole excepting which all other members have naked singularity. We analyze some properties of the region near singularity by studying a natural family of 2-surfaces. We establish that these have the topology of the 2-sphere by an application of the Gauss-Bonnet theorem. By computing the area, we establish that the singular region is `point-like'. Isometric embedding of these surfaces in the three dimensional Euclidean space is used to distinguish the two types of deviations from spherical symmetry.
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How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as background 2 papers
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The transformation ([ref]) was originally proposed by Zipoy [ref] and Voorhees [ref] and has been investigated in several works (see, for instance, [ref] and references therein).
Generating static perfect-fluid solutions of Einstein's equations · The vacuum q-metric · 0.84
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Several physical properties of the $q-$metric have been investigated in the literature (see, for instance, [ref] and references therein).
Motion of test particles in the field of a naked singularity · The $q-$metric · 1.00
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