In this paper we formulate the relationship between force-free electrodynamics and foliations. The background metric, is considered predetermined and electrically neutral, but otherwise arbitrary. As it turns out, solutions to force-free electrodynamics is intimately connected to the existence of foliations of a spacetime with prescribed properties. We also prove a local existence and uniqueness theorem and provide a recipe for constructing the unique solution/class of solutions when certain conditions are met. We clarify the theorem with examples. We are also able to also prove a singularity theorem for when non-null solutions approach the null limit. Here too, we construct an explicit example to illustrate the singularity theorem.

中文翻译：

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任意时空中的无力电动力学和叶理

在本文中，我们阐述了无力电动力学和叶理之间的关系。背景度量被认为是预定的和电中性的，但在其他方面是任意的。事实证明，无力电动力学的解决方案与具有规定特性的时空叶理的存在密切相关。我们还证明了局部存在性和唯一性定理，并提供了在满足某些条件时构建唯一解/解类的方法。我们用例子阐明定理。我们还能够证明当非零解接近零极限时的奇点定理。在这里，我们也构造了一个明确的例子来说明奇点定理。