The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Generalization of a Theorem by Goldberg and Sachs
Abstract
A connection is established between algebraic degeneracy of the Weyl tensor, the existence of a null geodesic shear-free congruence, and certain restrictions on the Ricci tensor which are weaker than the gravitational equations for empty space. The result is roughly, with some important qualifications, that any two of these conditions imply the third. These restrictions on the metric are shown to be invariant under conformal transformations.
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“It still is true 18,39 that, when a PND k of the electromagnetic field tensor is shear-free and geodesic, then the Weyl tensor is algebraically special, but the reverse no longer holds.”
From Algebraically special Einstein–Maxwell fields (2017) · cites this paper as [39]
In the citing paper
“It still is true 18,39 that, when a PND k of the electromagnetic field tensor is shear-free and geodesic, then the Weyl tensor is algebraically special, but the reverse no longer holds.”
From Algebraically special Einstein–Maxwell fields (2017) · cites this paper as [39]
Citations
Cites
An Approach to Gravitational Radiation by a Method of Spin Coefficients
Newman, E., & Penrose, R. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1724257 · Cited by 2,702
Research works printed but not linked: 4
- 1962, Acta Physica Polonica, 22, 13
- 1961, Proc. Roy. Soc. (London), A264, 309
- 1961, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 9, 543
- 1961, J. Math. Phys., 2, 290, 10.1063/1.1703712 · DOI · Paper page
Cited by
Algebraically special Einstein–Maxwell fields
Van den Bergh, N. (2017) · General Relativity and Gravitation · doi:10.1007/s10714-016-2171-x · Cited by 11
Metadata
- Authors
- Robinson, I., & Schild, A.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1963-04-01
- Volume
- 4
- Issue
- 4
- Pages
- 484-489
- ISSN
- 0022-2488
- 1089-7658
- Cited by
- 56
- References
- 1
- Language
- en
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Cite CoChat for the checks on this page, and the paper for its own findings.
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- CoChat. (2026). Citation check: Generalization of a Theorem by Goldberg and Sachs. https://app.cochat.ai/papers/10.1063/1.1703980
- The paper
- Robinson, I., & Schild, A. (1963). Generalization of a Theorem by Goldberg and Sachs. Journal of Mathematical Physics. https://doi.org/10.1063/1.1703980
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
