On Tensorial Concomitants and the Non-Existence of a
Gravitational Stress-Energy Tensor

Curiel, Erik (2009) On Tensorial Concomitants and the Non-Existence of a
Gravitational Stress-Energy Tensor.

Abstract

Based on an analysis of what it may mean for one tensor to depend in
the proper way on another, I prove that, under certain natural
conditions, there can be no tensor whose interpretation could be
that it represents gravitational stress-energy in general
relativity. It follows that gravitational energy, such as it is in
general relativity, is necessarily non-local. Along the way, I
prove a result of some interest in own right about the structure of
the associated jet bundles of the bundle of Lorentz metrics over
spacetime.