On the Causal Propagation of Fields

TL;DR

This paper introduces geometric criteria using superenergy tensors to determine the causal propagation of various physical fields across different spacetime dimensions, unifying and simplifying existing conservation theorems.

Contribution

It develops a universal, easy-to-apply method for analyzing causal propagation and conservation laws for diverse fields in arbitrary spacetimes, including Einstein spaces.

Findings

Provides new criteria for causal propagation of fields.

Establishes a conservation theorem for gravitational fields in N-dimensional spacetimes.

Offers simplified proofs for conservation laws of various massless and massive 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.