Through an exhaustive search, we produce a five-parameter family of propagation identities for the closed conformal Killing–Yano (cCYK) equation on two-forms, which hold on an Einstein cosmological vacuum spacetime in any dimension n > 4. It is well-known that spacetimes admitting a non-degenerate two-form of this type are exhausted by the Kerr-NUT-(A)dS family of exact higher dimensional black hole solutions. As a consequence, we identify a set of necessary and sufficient conditions ensuring that the cosmological vacuum development of an initial data set for Einstein’s field equations admits a cCYK two-form. We refer to these conditions as closed conformal Killing–Yano initial data equations. The four-dimensional case is special and is treated separately, where we can also handle the conformal Killing–Yano equation without the closed condition.

中文翻译：

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Closed conformal Killing–矢野初始数据

通过详尽的搜索，我们为封闭适形杀伤–矢野(cCYK) 双形式方程，它在任何维度上都适用于爱因斯坦宇宙学真空时空n> 4. 众所周知，允许这种类型的非退化二维形式的时空被 Kerr-NUT-(A)dS 系列的精确高维黑洞解穷尽了。因此，我们确定了一组必要条件和充分条件，确保爱因斯坦场方程初始数据集的宇宙学真空发展允许 cCYK 双形式。我们将这些条件称为closed conformal Killing–矢野初始数据方程式。四维情况比较特殊，单独处理，也可以处理不带封闭条件的保形Killing-Yano方程。