期刊
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
卷 2, 期 1, 页码 41-61出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219887805000491
关键词
tensor classification; Lorentz geometry; alignment; Weyl tensor
We develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that the alignment condition is equivalent to the principal null direction equation. In 4 dimensions this recovers the usual Petrov types are recovered. For higher dimensions we prove that, in general, a Weyl tensor does not possess any aligned directions. We then go on to describe a number of additional algebraic types for the various alignment configurations. For the case of second-order symmetric (Ricci) tensors, we perform the classification by considering the geometric properties of the corresponding alignment variety.
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