Abstract:This work provides a counterexample to the previously asserted non--existence of future null lines in strongly causal spacetimes $(M, \mathbf{g})$ foliated by a past--omniscient timelike foliation $\mathcal{F}$ with a compact leaf space $Q$. We introduce a new hypothesis requiring the timelike vector field that defines $\mathcal{F}$ to be causally decreasing. Under this condition, the causality requirement on $M$ can be relaxed to the distinguishing level. In the absence of this hypothesis, we demonstrate that more restrictive conditions, such as global hyperbolicity, are necessary to ensure the absence of future null lines. Finally, we derive sufficient conditions on the scale function of Generalized Robertson--Walker (GRW) spacetimes to ensure that the natural timelike vector field is causally decreasing, thereby guaranteeing the non--existence of future null lines.
From: Alfredo Bautista [view email]
[v1]
Tue, 2 Jun 2026 19:15:49 UTC (16 KB)
[v2]
Thu, 25 Jun 2026 10:10:15 UTC (18 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。