Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor

Details Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor

2010-08-16

arxiv.org/abs/1008.2716v3

Class.Quant.Grav.27:222001,2010; Erratum-ibid.28:129501,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages. Many errata corrected, including a computational mistake with relevant consequences. I have highlighted all the chang

Scientific paper

10.1088/0264-9381/27/22/222001 1

The algebraic classification of the Weyl tensor in arbitrary dimension n is recovered by means of the principal directions of its "superenergy" tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in general dimension can be achieved.

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