On the algebraic types of the Bel-Robinson tensor

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.

21 pages

References in corpus (5)

• Super-energy tensors
• Dynamical laws of superenergy in General Relativity
• A Rainich-like approach to the Killing-Yano tensors
• Unique characterization of the Bel-Robinson tensor
• Aligned electric and magnetic Weyl fields

Cited by in corpus (8)

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• Obtaining the Weyl tensor from the Bel-Robinson tensor
• On the super-energy radiative gravitational fields
• On the energy content of electromagnetic and gravitational plane waves through super-energy tensors
• Obtaining the multiple Debever null directions