AI 中文总结
研究线性化引力中诺特定理能量 - 动量张量非唯一性问题，通过诺特定理第一定理推导数学框架，无需‘改进’项，能影响拉格朗日比例部分，比较常见表达式并证明可得到对称无迹张量，讨论结果影响及与非唯一性问题的关系。
AI 中文摘要
能量 - 动量张量是标准物理场论（如电动力学和杨 - 米尔斯理论）中唯一确定的基础对象。在广义相对论，特别是线性化引力中，源于诺特定理第一定理的能量 - 动量张量所需对称性明确，但存在长期的非唯一性问题，文献中有众多不同表达式，尚无共识。近期超势‘改进’方法不足以解决线性化引力中能量 - 动量张量的非唯一性问题。本文利用诺特定理第一定理推导线性化引力中诺特定理能量 - 动量张量一般集的数学框架，包含所有能从诺特流产生线性化爱因斯坦场方程的能量 - 动量张量，无需‘改进’项。此结果有诸多优点，还能影响能量 - 动量张量的拉格朗日比例部分。将众多常见引力能量 - 动量表达式与这些一般结果比较，评估其是否为诺特定理的。用对称性和无迹性等标准证明可从诺特流直接得到同时对称且无迹的能量 - 动量张量，并从一般结果导出该表达式。讨论了这些结果的影响及其与非唯一性问题的关系。
英文摘要
Energy-momentum tensors are foundational objects which are uniquely defined in standard physical field theories such as electrodynamics and Yang-Mills theory. In general relativity, and in particular linearized gravity where symmetries required for an energy-momentum tensor derived from Noether's first theorem are well defined, there exists a long standing non-uniqueness problem; numerous distinct energy-momentum expressions exist in the literature, and there is not consensus which, if any, is the unique expressions for the theory. Recently, the viability of the superpotential `improvement' method was shown to be insufficient for addressing the non-uniqueness problem of energy-momentum tensors in linearized gravity. In the present article, the mathematical framework for the general set of Noetherian energy-momentum tensors in linearized gravity is derived using Noether's first theorem, which consists of all possible energy-momentum tensors from the Noether current which yield the linearized Einstein field equations in the corresponding Euler-Lagrange equation of the Noether identity without introducing any `improvement' terms. This result has several advantages in addition to not requiring `improvements', such as the ability to impact the Lagrangian proportional piece of the energy-momentum tensor. Numerous common published gravitational energy-momentum expressions are then compared to these general results to assess which can be classified as Noetherian, and which cannot. Standard physical criteria such as symmetry and tracelessness are then used to prove that it is possible to directly obtain an energy-momentum tensor which is simultaneously symmetric and traceless from the Noether current; such an expression is derived from the general results. Consequences of these results and their relation to the aforementioned non-uniqueness problem are discussed.
Journal refPhysica Scripta 99 035258 (2024)
