Sectional curvature and the energy-momentum tensor

Graham Stanley Hall, L. McNay

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Many years ago Ehlers and Kundt showed that a spacetime M is an Einstein space if and only if the sectional curvatures of any pair of orthogonal non-null 2-spaces at any point of M are equal. This paper generalizes this result by first showing a very straightforward relation between the sectional curvatures of such orthogonal pairs of 2-spaces and the trace-free part of the Ricci tensor and then by establishing for each algebraic (Segre) type of the energy-momentum tensor precisely which orthogonal pairs of non-null 2-spaces have the same sectional curvature. The results are described in a manifold theoretic sense and are tabulated for each Segre type.

Original languageEnglish
Pages (from-to)1493-1502
Number of pages9
JournalClassical and Quantum Gravity
Issue numberMay
Publication statusPublished - 2005




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