Unique characterization of the Bel--Robinson tensor

doi:10.1088/0264-9381/21/14/012

Unique characterization of the Bel–Robinson tensor

G Bergqvist et al 2004 Class. Quantum Grav. 21 3499-3503 doi: 10.1088/0264-9381/21/14/012

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G Bergqvist¹ and P Lankinen²
¹ Matematiska institutionen, Linköpings universitet, SE-581 83 Linköping, Sweden
² Department of Mathematics and Physics, Mälardalen University, SE-721 23 Västerås, Sweden
E-mail: gober@mai.liu.se and paul.lankinen@mdh.se

Abstract. We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel–Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

PACS numbers: 04.20.Cv, 04.20.Gz, 02.40.Ky

Print publication: Issue 14 (21 July 2004)
Received 13 May 2004
Published 23 June 2004

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Unique characterization of the Bel–Robinson tensor

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