In this paper, we study geometrical properties of marginally trapped surfaces in gravitational collapse, using a semi-tetrad covariant formalism, that provides a set of geometrical and matter variables. We first define a generalization (in a sense to be specified in the introduction) of LRS II spacetime — which we call NNF spacetimes — and show that the marginally trapped surfaces in NNF spacetimes (and the 3-surfaces they foliate) are topologically equivalently those of LRS II spacetimes. We then study the evolution of MTTs (3-surfaces foliated by marginally trapped surfaces), extending earlier work on LRS II spacetimes to NNF spacetimes, and in general any 4-dimensional spacetime. In addition, we perform a stability analysis for the marginally trapped surfaces in this formalism, using simple spacetimes as examples to demonstrate the applicability of our approach.

中文翻译：

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零正态叶理时空中的边缘捕获表面：LRS II 时空的一步概括

在本文中，我们使用提供一组几何和物质变量的半四分体协变形式来研究重力坍塌中边缘被困表面的几何特性。我们首先定义 LRS II 时空（我们称之为 NNF 时空）的泛化（在某种意义上将在引言中指定），并表明 NNF 时空中边缘被困的表面（以及它们叶形的 3-表面）在拓扑上等价于那些LRS II 时空。然后，我们研究 MTT（由边缘捕获的表面形成叶状体的 3 个表面）的演变，将早期关于 LRS II 时空的工作扩展到 NNF 时空，以及通常的任何 4 维时空。此外，我们对这种形式中的边缘被困表面进行了稳定性分析，