再论彼得罗夫D真空空间：恒等式和不变分类
Petrov D vacuum spaces revisited: Identities and Invariant Classification
摘要：
对于PetrovD真空空间，利用GHP形式，通过系统而透明的分析，重新导出了两个简单的恒等式，并得到了一些新的恒等式。这给出了一个完整的对合表的四个GHP衍生物的四个GHP自旋系数和一个外尔张量分量。它直接从这些结果，理论上限的顺序协变微分的黎曼张量所需的Karlhede分类这些空间减少到两个。
英文摘要：
For Petrov D vacuum spaces, two simple identities are rederived and some new identities are obtained, in a manageable form, by a systematic and transparent analysis using the GHP formalism. This gives a complete involutive set of tables for the four GHP derivatives on each of the four GHP spin coefficients and the one Weyl tensor component. It follows directly from these results that the theoretical upper bound on the order of covariant differentiation of the Riemann tensor required for a Karlhede classification of these spaces is reduced to two.
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