Classification of the Weyl Tensor in Higher Dimensions

Details Classification of the Weyl Tensor in Higher Dimensions Classification of the Weyl Tensor in Higher Dimensions

2004-01-03

arxiv.org/abs/gr-qc/0401008v2

Class.Quant.Grav.21:L35-L42,2004

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages; submitted to Class Quant Grav. References updated

Scientific paper

10.1088/0264-9381/21/7/L01

We discuss the algebraic classification of the Weyl tensor in higher dimensional Lorentzian manifolds. This is done by characterizing algebraically special Weyl tensors by means of the existence of aligned null vectors of various orders of alignment. Further classification is obtained by specifying the alignment type and utilizing the notion of reducibility. For a complete classification it is then necessary to count aligned directions, the dimension of the alignment variety, and the multiplicity of principal directions. The present classification reduces to the classical Petrov classification in four dimensions. Some applications are briefly discussed.

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