AI 中文总结
针对广义相对论中完整协变能动张量的长期问题，该研究通过将度规高阶微分项纳入引力作用量，提出广义正则形式的引力能动张量协变定义，可在任意坐标系正确获取引力能量。
AI 中文摘要
在广义相对论中定义完整且协变的能动张量是长期受关注的问题，一种广泛尝试的方法是在渐近洛伦兹系中将其定义为赝张量。本文提出了广义正则形式下引力能动张量的完整协变定义，关键在于将度规张量的高阶微分项纳入引力作用量，以一致地推导能动张量；这种完全协变形式确保在任意坐标系（包括极坐标和渐近洛伦兹系）中都能正确得到引力能量。
英文摘要
Defining a complete and covariant energy-momentum tensor in general relativity is a longstanding issue of concern. A widely attempted approach is to define it as a pseudo-tensor in an asymptotic Lorentz system. In this paper, we present a complete covariant definition of the gravitational energy-momentum tensor in the generalized canonical form. The key is incorporate higher-order differential terms of the metric tensor into the gravitational action in order to derive the energy-momentum tensor consistently. This completely covariant form ensures that the gravitational energy is correctly obtained in any coordinate system, including polar coordinates and asymptotic Lorentz systems.
