0908.3322 (Erik Curiel)

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

Erik Curiel

The question of the existence of gravitational stress-energy in general
relativity has exercised investigators in the field since the inception of the
theory. Folklore has it that no adequate definition of a localized
gravitational stress-energetic quantity can be given. Most arguments to that
effect invoke one version or another of the Principle of Equivalence. I argue
that not only are such arguments of necessity vague and hand-waving but, worse,
are beside the point and do not address the heart of the issue. Based on a
novel 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.

View original: http://arxiv.org/abs/0908.3322