Algebraic Rainich theory and antisymmetrization in higher dimensions
Algebraic Rainich theory and antisymmetrization in higher dimensions
复制标题
高维代数 Rainich 理论和反对称
DOI：
10.1088/0264-9381/19/12/316
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发表时间：
2002
影响因子：
3.5
通讯作者：
A. Hoglund
中科院分区：
文献类型：
--
作者：
G. Bergqvist;A. Hoglund
经典的 Rainich(–Misner–Wheeler) 理论给出了能量动量张量 T 成为四维麦克斯韦场（2 型）的充分必要条件。通过爱因斯坦方程，这些条件可以用里奇张量来表达，从而为时空几何成为爱因斯坦-麦克斯韦时空提供了条件。其中一个条件是T2与度量成正比，之前已经在任意维度上证明了满足该条件的任何张量都是简单p型的超能张量。在这里，我们通过反对称研究了高维中一般 p 型的代数 Rainich 条件及其与恒等式的关系。使用反对称技术，我们找到了这些一般（非简单）形式的超能张量的新恒等式，并且在某些情况下我们还证明了相反的情况：恒等式足以确定形式。作为一个例子，我们获得了经典莱尼奇理论到五个维度的完整推广。
The classical Rainich(–Misner–Wheeler) theory gives necessary and sufficient conditions on an energy–momentum tensor T to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations, these conditions can be expressed in terms of the Ricci tensor, thus providing conditions for a spacetime geometry to be an Einstein–Maxwell spacetime. One of the conditions is that T2 is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple p-form. Here we examine algebraic Rainich conditions for general p-forms in higher dimensions and their relations to identities by antisymmetrization. Using antisymmetrization techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse: that the identities are sufficient to determine the form. As an example we obtain the complete generalization of the classical Rainich theory to five dimensions.