Sectional curvature and the energy-momentum tensor

Graham Stanley Hall, L. McNay

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)1493-1502
Number of pages9
JournalClassical and Quantum Gravity
Volume22
Issue numberMay
DOIs
Publication statusPublished - 2005

Keywords

  • GENERAL-RELATIVITY
  • CANONICAL FORMS

Cite this