Galloway Gregory, Ling Eric
University of Miami, Coral Gables, FL USA.
Copenhagen Centre for Geometry and Topology (GeoTop), Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
Commun Math Phys. 2025;406(2):25. doi: 10.1007/s00220-024-05210-4. Epub 2025 Jan 11.
In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of MOTS which generate totally geodesic null hypersurfaces. Depending on our starting assumptions, we obtain either local or global rigidity results. We apply our arguments to cosmological spacetimes (i.e., spacetimes with compact Cauchy surfaces) and scenarios involving topological censorship.
在本文中，我们研究彭罗斯奇点定理的刚性方面。具体而言，我们旨在回答以下问题：如果一个时空满足彭罗斯奇点定理的假设，但用弱俘获面代替俘获面，那么当该时空是类光测地线完备时，关于整体时空结构能得出什么结论？在此情形下，我们表明我们得到了一组生成完全测地类光超曲面的MOTS叶状结构。根据我们的初始假设，我们得到了局部或全局的刚性结果。我们将我们的论证应用于宇宙学时空（即具有紧致柯西曲面的时空）以及涉及拓扑审查的情形。
