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.

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)

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Cited by in corpus (7)

• Algebraic classification of higher dimensional spacetimes based on null alignment
• Interpreting spacetimes of any dimension using geodesic deviation
• Asymptotic Structure with a positive cosmological constant
• A novel characterisation of gravitational radiation in asymptotically flat space-times
• Algebraic classification of 2+1 geometries: a new approach
• Second-order symmetric Lorentzian manifolds II: structure and global properties
• Algebraic classification of the gravitational field in general metric-affine geometries