G S Hall and Lucy MacNay
Department of Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen AB24 3UE, UK
Classical and Quantum Gravity Create an alert RSS this journal
G S Hall and Lucy MacNay 2005 Class. Quantum Grav. 22 1493
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.
Issue 9 (7 May 2005)
Received 15 December 2004
,
in final form 10 February 2005
Published 6 April 2005
G S Hall and Lucy MacNay 2005 Class. Quantum Grav. 22 1493
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