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arXiv · 0807.0181

On the algebraic types of the Bel-Robinson tensor

Joan J. Ferrando·Juan A. Sáez
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Abstract

The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov-Bel types and the additional ones are intrinsically characterized in terms of the sole Bel-Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel-Robinson tensor in regular cases.

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Joan J. Ferrando, Juan A. Sáez. 2008-07-01. On the algebraic types of the Bel-Robinson tensor. https://doi.org/10.1007/s10714-008-0738-x

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