Sectional curvature and the energy momentum tensor

Details Sectional curvature and the energy momentum tensor Sectional curvature and the energy momentum tensor

May 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cqgra..22.1493h&link_type=abstract

Classical and Quantum Gravity, Volume 22, Issue 9, pp. 1493-1502 (2005).

Physics

1

Scientific paper

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.

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