任意维的能量条件
Energy conditions in arbitrary dimensions
摘要：
在不指定局部未来和过去方向的情况下，全面研究了任意$n(\ge 3)$维物质场的能量条件。我们将能量-动量张量分类为霍金-埃利斯I型到IV型的$n$维对应物，其中III型由比霍金和埃利斯以及其他作者在给定时空中识别III型能量-动量张量所采用的形式更有用的形式定义。我们还提供了必要和充分条件，类型I和II的能量动量张量的正交分量的标准形式的不平等，并表明，类型III和IV违反所有标准的能量条件。最后，我们研究了一组物理激励的物质场的能量条件。
英文摘要：
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.
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