A Coley et al 2004 Class. Quantum Grav. 21 L35 doi:10.1088/0264-9381/21/7/L01
Classification of the Weyl tensor in higher dimensions
FREE ARTICLEA Coley1, R Milson1, V Pravda2 and A Pravdová2
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We discuss the algebraic classification of the Weyl tensor in higher-dimensional Lorentzian manifolds. This is done by characterizing algebraically special Weyl tensors by means of the existence of aligned null vectors of various orders of alignment. Further classification is obtained by specifying the alignment type and utilizing the notion of reducibility. For a complete classification it is then necessary to count aligned directions, the dimension of the alignment variety and the multiplicity of principal directions. The present classification reduces to the classical Petrov classification in four dimensions. Some applications are briefly discussed.
- PACS
- MSC
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15A72 Vector and tensor algebra, theory of invariants (See also 13A50, 14L24)
- Subjects
- Dates
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Issue 7 (7 April 2004)
Received 17 December 2003
Published 8 March 2004
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Classification of the Weyl tensor in higher dimensions
A Coley et al 2004 Class. Quantum Grav. 21 L35
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