Unique characterization of the Bel–Robinson tensor

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.