将 van Stockum 尘埃与 Papapetrou 真空匹配
Matching van Stockum dust to Papapetrou vacuum
AI总结：
本文解决了 van Stockum 尘埃与 Papapetrou 真空匹配的长期问题，证明了二者的相互匹配关系，揭示了边界确定条件，并通过与 Ehlers 及 Kramer-Neugebauer 变换的联系给出了具有预设边界的尘埃云实例。
摘要：
针对这一长期存在的问题，我们证明了每个 van Stockum 尘埃均可匹配至一个 1 参数的非静态 Papapetrou 真空度量族，反之亦然。若边界存在，其由真空侧特定一阶不变量的消失所决定。此外，我们建立了与 Ehlers 及 Kramer-Neugebauer 变换的联系，借此可寻找具有预设边界的尘埃云。显式示例包括 Bonnor 度量、Lanczos-van Stockum 尘埃度量的新真空外部，以及具有非平凡拓扑的尘埃云。
英文摘要：
Addressing a long-standing problem, we show that every van Stockum dust can be matched to a 1-parametric family of non-static Papapetrou vacuum metrics, and the converse. The boundary, if existing, is determined by vanishing of certain first-order invariant on the vacuum side. Moreover, we establish a relation to Ehlers and Kramer--Neugebauer transformations, which allows us to look for dust clouds with a prescribed boundary. Explicit examples include the Bonnor metric and a new vacuum exterior to the Lanczos--van Stockum dust metric, as well as dust clouds with nontrivial topology.
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