Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor
Abstract
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.
Keywords
Cite
@article{arxiv.1008.2716,
title = {Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor},
author = {José M. M. Senovilla},
journal= {arXiv preprint arXiv:1008.2716},
year = {2011}
}
Comments
9 pages. Many errata corrected, including a computational mistake with relevant consequences. I have highlighted all the changes in a different color (blue). The main changes concern point (iv) in Proposition 1, and its consequences concerning the characterization of types III, II and D. A reference has been added as well as new acknowledgements. (A corrigendum has been sent to CQG)