  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, which, \emph{en passant}, provides a precise characterization of
the idea of a `geometric object', 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. I conclude by showing that my results also imply that, under a
few natural conditions, the Einstein field equation is the unique equation
relating gravitational phenomena to spatiotemporal structure, and discuss how
this relates to the non-localizability of gravitational stress-energy. The main
theorem proven underlying all the arguments is considerably stronger than the
standard result in the literature used for the same purposes (Lovelock's
theorem of 1972): it holds in all dimensions (not only in four); it does not
require an assumption about the differential order of the desired concomitant
of the metric; and it has a more natural physical interpretation.
