The universal ‘energy’ operator

Abstract

The ‘positive square’ of any tensor is presented in a universal and unified manner, valid in Lorentzian manifolds of arbitrary dimension, and independently of any (anti)-symmetry properties of the tensor. For rank-m tensors, the positive square has rank 2m. Positive here means future, that is to say, satisfying the dominant property. The standard energy–momentum and super-energy tensors are recovered as appropriate parts of the general square. A richer structure of principal null directions arises.