Spinor classification of the Weyl tensor in five dimensions

Details Spinor classification of the Weyl tensor in five dimensions Spinor classification of the Weyl tensor in five dimensions

2010-08-17

arxiv.org/abs/1008.2955v1

Class.Quant.Grav.27:245013,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

40 pages

Scientific paper

10.1088/0264-9381/27/24/245013

We investigate the spinor classification of the Weyl tensor in five dimensions due to De Smet. We show that a previously overlooked reality condition reduces the number of possible types in the classification. We classify all vacuum solutions belonging to the most special algebraic type. The connection between this spinor and the tensor classification due to Coley, Milson, Pravda and Pravdov\'a is investigated and the relation between most of the types in each of the classifications is given. We show that the black ring is algebraically general in the spinor classification.

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