CAUSAL TENSORS AND RAINICH'S CONDITIONS

Abstract

The mathematical properties of causal tensors,1 which are the tensors satisfying the dominant property (generalization of the dominant energy condition), were presented. The whole class of the so-called superenergy tensors2, including in particular the Bel-Robinson tensor, are causal tensors. Conversely, the superenergy tensors are the basic building blocks of all causal tensors1. Actually, the superenergy tensors of simple forms are intimately related to conformally Lorentz transformations as they leave the null cone invariant.1 This provides, in particular, a wide generalization of the algebraic Rainich conditions1 in arbitrary dimension and for many different fields. See 1,2 and references therein for details.