ALIGNMENT AND ALGEBRAICALLY SPECIAL TENSORS IN LORENTZIAN GEOMETRY
By Robert Milson, Alan Coley, V. Pravda, A. Pravdová. 2004
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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.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f0205b68cd5c6a043739bb3f999c4898eaeab3f7
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Citations in the corpus
- From Navier-Stokes to Einstein (2011, result): “This may enable a connection of the present work with the large literature on algebraically special spacetimes [36–38].”