Tensors,Spinors and Multivectors in the Petrov Classification |
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Authors: | José M Pozo Josep M Parra |
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Institution: | (1) SYRTE Observatoire de Paris – CNRS, 61, Avenue de l’Observatoire, F-75014 Paris, France;(2) Present address: Cilab, Departament de Tecnologia, Universitat Pompeu Fabra, Passeig de Circumvallaci, 8 Edifici Frana, E-08003 Barcelona, Spain;(3) Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain |
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Abstract: | The Petrov classification of the Weyl tensor is revised in its two main approaches: bivector endomorphism and principal null
directions. A more transparent presentation is obtained by the use of the real geometric Clifford algebra, where the consideration
of bivectors
(E) integrated in the full Grassmann space
(E) is basic. This language establishes a more close relationship between both approaches and enables the introduction of a
new canonical tensorial form for the Weyl tensor which is directly comparable with the spinorial classification. Special care
has been given to present properties in its more general form, without specific restriction to a given dimensionality or to
a given signature, whenever possible. |
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Keywords: | " target="_blank"> Weyl tensor Petrov classification Clifford algebra multivectors 2-spinors |
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