Higher dimensional bivectors and classification of the Weyl operator

Details Higher dimensional bivectors and classification of the Weyl operator Higher dimensional bivectors and classification of the Weyl operator

2009-09-07

arxiv.org/abs/0909.1160v2

Class.Quant.Grav.27:015002,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages; v2: some notation changed, typos fixed; CQG accepted

Scientific paper

10.1088/0264-9381/27/1/015002

We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise to a refinement in dimensions higher than four of the usual alignment (boost-weight) classification, in terms of the irreducible representations of the spins. We are consequently able to define a number of new algebraically special cases. In particular, the classification in five dimensions is discussed in some detail. In addition, utilizing the (refined) algebraic classification, we are able to prove some interesting results when the Weyl tensor has (additional) symmetries.

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