理想点、定向完备化与最大延拓史瓦西时空案例
Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime
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中文总结 AI 辅助
该研究探讨洛伦兹预长度空间的定向完备化，证明其在特定假设下与GKP未来因果完备化一致，并将其应用于克鲁斯卡尔–塞凯赖什时空的定向完备化刻画。
中文摘要 AI 辅助
我们研究洛伦兹预长度空间的定向完备化，证明在涵盖光滑整体双曲时空情形的若干自然假设下，其与Geroch–Kronheimer–Penrose的未来因果完备化一致。此外，我们通过径向类光测地线刻画克鲁斯卡尔–塞凯赖什（Kruskal–Szekeres）时空的定向完备化，给出研究结果的应用。
英文摘要
We study the directed completion of Lorentzian pre-length spaces, and we show that, under some natural assumptions which cover the case of smooth globally hyperbolic spacetimes, it coincides with the future causal completion of Geroch--Kronheimer--Penrose. Moreover, we provide applications of our findings by characterizing the directed completion of the Kruskal--Szekeres spacetime in terms of its radial null geodesics.
