The energy conditions are studied, in the relativistic astrophysical setting, for higher-dimensional Hawking–Ellis Type I and Type II matter fields. The null, weak, dominant and strong energy conditions are investigated for a higher-dimensional inhomogeneous, composite fluid distribution consisting of anisotropy, shear stresses, non-vanishing viscosity as well as a null dust and null string energy density. These conditions are expressed as a system of six equations in the matter variables where the presence of the higher dimension $N$ is explicit. The form and structure of the energy conditions is influenced by the geometry of the $(N-2)$-sphere. The energy conditions for the higher-dimensional Type II fluid are also generated, and it is shown that under certain restrictions the conditions for a Type I fluid are regained. All previous treatments for four dimensions are contained in our work.

中文翻译：

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高维非均匀复合流体：能量条件

在相对论天体物理学背景下，研究了高维霍金-埃利斯 I 型和 II 型物质场的能量条件。研究了由各向异性、剪切应力、非消失粘度以及零尘埃和零弦能量密度组成的高维非均匀复合流体分布的零能量、弱能量、主导能量和强能量条件。这些条件表示为物质变量中的六个方程的系统，其中高维 $N$ 的存在是明确的。能量条件的形式和结构受$(N-2)$-球体的几何形状的影响。更高维度的 II 型流体的能量条件也被生成，并且表明在某些限制下，I 型流体的条件被恢复。