Uniqueness of the metric from the Weyl and energy‐momentum tensors

It is shown that for a general space‐time in Einstein’s theory (with the term ‘‘general’’ being precisely defined) the Weyl tensor and energy‐momentum tensor determine the metric up to a constant conformal factor. One of the conclusions may be interpreted as a generalization of the well‐known Brinkm...

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Bibliographic Details
Published in:Journal of mathematical physics 1987-08, Vol.28 (8), p.1837-1839
Main Authors: Hall, G. S., Rendall, A. D.
Format: Article
Language:English
Subjects:
Classical general relativity
Exact sciences and technology
General relativity and gravitation
Physics
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Summary:It is shown that for a general space‐time in Einstein’s theory (with the term ‘‘general’’ being precisely defined) the Weyl tensor and energy‐momentum tensor determine the metric up to a constant conformal factor. One of the conclusions may be interpreted as a generalization of the well‐known Brinkmann theorem characterizing p p waves i n v a c u o.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.527443