On the causal propagation of fields

By using geometric methods and superenergy tensors, we find new simple crit eria for the causal propagation of physical fields in spacetimes of any dim ension. The method can be applied easily to many different theories and to arbitrary fields (such as scalar or electromagnetic fields). In particular, it provides a conservation theorem for the free gravitational field in all N-dimensional spacetimes conformally related to Einstein spaces (including the Ricci-flat case). In general relativity, our criteria provide simple p roofs and a unified treatment of conservation theorems for neutrinos, photo ns, 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 tre atment under certain circumstances.