Unique characterization of the Bel-Robinson tensor

Details Unique characterization of the Bel-Robinson tensor Unique characterization of the Bel-Robinson tensor

2004-03-04

arxiv.org/abs/gr-qc/0403024v3

Class.Quant.Grav. 21 (2004) 3499-3504

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

extended version, 13 pages, shorter version published in Class.Quant.Grav

Scientific paper

10.1088/0264-9381/21/14/012

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.

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