AI 中文总结
研究任意维度静电系统相关的自然(0,3)张量，源于科顿与外尔分解比较，扩展已知恒等式，证明其无迹且有特定代数对称性，在电场与消逝函数梯度共线假设下研究性质并获简化表达式，还扩展相关结果与推导恒等式。
AI 中文摘要
我们引入了一个与任意维度静电系统相关的自然(0,3)张量。该张量源于黎曼曲率张量的科顿分解和外尔分解的比较，扩展了三维和四维中先前已知的几个恒等式。我们证明它是完全无迹的，并且满足与科顿张量相同的代数对称性。在电场与消逝函数梯度共线的自然假设下，我们进一步研究其性质，得到一个简化表达式。在此过程中，我们将一个边界共线性结果扩展到任意维度，并推导了几个在静电系统研究中可能有用的恒等式。
英文摘要
We introduce a natural (0,3)-tensor associated with electrostatic systems in arbitrary dimensions. This tensor arises from the comparison between the Cotton and Weyl decompositions of the Riemann curvature tensor and extends several identities previously known in dimensions three and four. We prove that it is totally trace-free and satisfies the same algebraic symmetries as the Cotton tensor. We further investigate its behavior under the natural assumption that the electric field is collinear with the gradient of the lapse function, obtaining a simplified expression. Along the way, we extend a boundary collinearity result to arbitrary dimensions and derive several identities that may be useful in the study of electrostatic systems.
