In this paper, we introduce the notion of a marginal tube, which is a hypersurface foliated by marginal surfaces. It generalises the notion of a marginally trapped tube and several notions of black hole horizons, for example trapping horizons, isolated horizons, dynamical horizons, etc. We prove that if every spacelike section of a marginal tube is a marginal surface, then the marginal tube is null. There is no assumption on the topology of the marginal tube. To prove it, we study the geometry of spacelike surfaces in a four-dimensional spacetime with the help of double null coordinate systems. The result is valid for arbitrary four-dimensional spacetimes, regardless of any energy condition.

中文翻译：

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边缘管和边缘表面的叶状结构

在本文中，我们介绍了边缘管的概念，边缘管是由边缘表面叶状排列的超曲面。它概括了边缘陷阱管的概念和黑洞视界的几个概念，例如陷阱视界、孤立视界、动力学视界等。我们证明了如果边缘管的每个类空间部分都是边缘表面，那么边缘管一片空白。边缘管的拓扑结构没有假设。为了证明这一点，我们借助双零坐标系研究了四维时空中类空表面的几何形状。无论任何能量条件如何，该结果都适用于任意四维时空。