Energy conditions for matter fields are comprehensively investigated in arbitrary $n(\ge 3)$ dimensions without specifying future and past directions locally. We classify an energy-momentum tensor into $n$-dimensional counterparts of the Hawking-Ellis type I to IV, where type III is defined by a more useful form than those adopted by Hawking and Ellis and other authors to identify the type-III energy-momentum tensor in a given spacetime. We also provide necessary and sufficient conditions for types I and II as inequalities for the orthonormal components of the energy-momentum tensor in a canonical form and show that types III and IV violate all the standard energy conditions. Lastly, we study energy conditions for a set of physically motivated matter fields.

中文翻译：

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任意维度的能量条件

在任意 $n(\ge 3)$ 维度上全面研究物质场的能量条件，而无需在本地指定未来和过去的方向。我们将能量动量张量分类为霍金-埃利斯 I 至 IV 型的 $n$ 维对应物，其中 III 型定义为比霍金和埃利斯以及其他作者采用的更有用的形式来识别 III 型给定时空中的能量-动量张量。我们还提供了类型 I 和 II 的充分必要条件，作为规范形式的能量-动量张量的正交分量的不等式，并表明类型 III 和 IV 违反了所有标准能量条件。最后，我们研究了一组物理驱动的物质场的能量条件。