We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex near the singularity corresponding to the ring singularity in the interior of the black hole. We then proceed to classify regular ambitoric $4$-orbifolds with some completeness assumptions. The tools developed also allow us to prove a partial classification of compact Riemannian 4-manifolds which admit a Killing $2$-form.

中文翻译：

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常规的4美元歧义符号：从黎曼·克尔到完整分类

我们表明，可以为Kerr黑洞度量的Riemannian类似物的共形结构赋予二元结构。然后，我们讨论矩量图的属性。特别地，我们观察到矩图图像在对应于黑洞内部的环奇点的奇点附近没有局部凸出。然后，我们使用一些完整性假设对常规的四元以上的四元数-双元进行分类。开发的工具还使我们能够证明紧凑型黎曼4流形的部分分类，这些流形允许使用Killing $ 2 $形式。