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The question of the existence of gravitational stress-energy in generalrelativity has exercised investigators in the field since the inception of thetheory. Folklore has it that no adequate definition of a localizedgravitational stress-energetic quantity can be given. Most arguments to thateffect invoke one version or another of the Principle of Equivalence. I arguethat 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 anovel analysis of what it may mean for one tensor to depend in the proper wayon another, which, \emph{en passant}, provides a precise characterization ofthe idea of a `geometric object', I prove that, under certain naturalconditions, there can be no tensor whose interpretation could be that itrepresents gravitational stress-energy in general relativity. It follows thatgravitational energy, such as it is in general relativity, is necessarilynon-local. Along the way, I prove a result of some interest in own right aboutthe structure of the associated jet bundles of the bundle of Lorentz metricsover spacetime. I conclude by showing that my results also imply that, under afew natural conditions, the Einstein field equation is the unique equationrelating gravitational phenomena to spatiotemporal structure, and discuss howthis relates to the non-localizability of gravitational stress-energy. The maintheorem proven underlying all the arguments is considerably stronger than thestandard result in the literature used for the same purposes (Lovelock'stheorem of 1972): it holds in all dimensions (not only in four); it does notrequire an assumption about the differential order of the desired concomitantof the metric; and it has a more natural physical interpretation.

On Geometric Objects, the Non-Existence of a Gravitational Stress-Energy Tensor, and the Uniqueness of the Einstein Field Equation