A note on matter superenergy tensors

We consider Bel-Robinson-like higher derivative conserved two-index tensors H(mu)(nu) in simple matter models, following a recently suggested Maxwell field version. In flat space, we show that they are essentially equivalent to the true stress tensors. In curved Ricci-flat backgrounds it is possible to redefine H(mu)(nu) so as to overcome non-commutativity of covariant derivatives, and maintain conservation, but they become model and dimension dependent, and generally lose their simple ‘BR’ form.