张量伴随与引力应力-能量张量的不存在性
On Tensorial Concomitants and the Non-Existence of a Gravitational Stress-Energy Tensor
摘要：
在广义相对论中，引力应力-能量的存在问题，从理论创立之初就一直困扰着该领域的研究者。Folklore认为，对于局部的引力应力-能量的量，不能给出一个适当的定义。这方面的大多数论点都援引了等效原则的一个或另一个版本。我认为，这种必要性的论点不仅含糊不清，而且更糟糕的是，离题了，没有解决问题的核心。基于对一个张量以适当的方式依赖于另一个张量可能意味着什么的新颖分析，我证明，在某些自然条件下，不可能有张量，其解释可能是它代表了广义相对论中的引力应力-能量。由此可见，引力能，就像在广义相对论中那样，必然是非定域的。一路上，我证明了一些自己的权利感兴趣的结果有关的结构，相关的喷丛的束洛伦兹度规在时空。
英文摘要：
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.
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