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On the algebraic types of the Bel–Robinson tensor

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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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Authors and Affiliations

  1. Departament d’Astronomia i Astrofísica, Universitat de València, 46100, Burjassot, València, Spain

    Joan Josep Ferrando

  2. Departament de Matemàtiques per a l’Economia i l’Empresa, Universitat de València, 46071, València, Spain

    Juan Antonio Sáez

Authors
  1. Joan Josep Ferrando
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  2. Juan Antonio Sáez
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Correspondence to Joan Josep Ferrando.

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Ferrando, J.J., Sáez, J.A. On the algebraic types of the Bel–Robinson tensor. Gen Relativ Gravit 41, 1695–1715 (2009). https://doi.org/10.1007/s10714-008-0738-x

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  • DOI: https://doi.org/10.1007/s10714-008-0738-x

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