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arXiv · 0906.3818

Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions

Marcello Ortaggio
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Abstract

An extension to higher dimensions of the Bel-Debever characterization of the Weyl tensor is considered. This provides algebraic conditions that uniquely determine the multiplicity of a Weyl aligned null direction (WAND), and thus the principal Weyl type, in a frame independent way. The specification of several "subtypes" is also encompassed by the criteria. We further comment on a Cartan-like geometrical interpretation of WANDs in terms of their invariance properties under parallel transport around infinitesimal loops. As a result, restrictions on the algebraic types permitted in spacetimes that admit a recurrent/covariantly constant vector field are outlined.

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Marcello Ortaggio. 2009-06-20. Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions. https://doi.org/10.1088/0264-9381%2F26%2F19%2F195015

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