On the Causal Propagation of Fields

Abstract

By using geometric methods and superenergy tensors, we find new simple criteria for the causal propagation of physical fields in spacetimes of any dimension. The method can be applied easily to many different theories and to arbitrary fields (such as scalar or electromagnetic ones). In particular, it provides a conservation theorem of the free gravitational field in all N-dimensional spacetimes conformally related to Einstein spaces (including vacuum solutions). In the case of general relativity, our criteria provide simple proofs and a unified treatment of conservation theorems for neutrinos, photons, electrons and all other massless and massive free spin n/2 fields. The uniqueness of the solution to the field equations also follows from our treatment under certain circumstances.