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General Relativity and Gravitation

, Volume 41, Issue 8, pp 1695–1715 | Cite as

On the algebraic types of the Bel–Robinson tensor

  • Joan Josep Ferrando
  • Juan Antonio Sáez
Research Article

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.

Keywords

Bel–Robinson tensor Gravitational superenergy Petrov–Bel classification 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Departament d’Astronomia i AstrofísicaUniversitat de ValènciaBurjassot, ValènciaSpain
  2. 2.Departament de Matemàtiques per a l’Economia i l’EmpresaUniversitat de ValènciaValènciaSpain

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