### Abstract

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 language | English |
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Pages (from-to) | 1493-1502 |

Number of pages | 9 |

Journal | Classical and Quantum Gravity |

Volume | 22 |

Issue number | May |

DOIs | |

Publication status | Published - 2005 |

### Keywords

- GENERAL-RELATIVITY
- CANONICAL FORMS

## Cite this

Hall, G. S., & McNay, L. (2005). Sectional curvature and the energy-momentum tensor.

*Classical and Quantum Gravity*,*22*(May), 1493-1502. https://doi.org/10.1088/0264-9381/22/9/001