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arXiv · 2605.21871

Refocusing spacetimes need not be strongly refocusing

Friedrich Bauermeister
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Abstract

We prove that there are globally hyperbolic spacetimes which are refocusing but not strongly refocusing. In fact, every globally hyperbolic strongly refocusing spacetime of dimension at least $3$ admits globally hyperbolic metrics which are refocusing but not strongly refocusing. This answers a question by Chernov, Kinlaw, and Sadykov. We then prove that globally hyperbolic spacetimes which are Legendrian refocusing (a notion introduced in this paper) admit globally hyperbolic strongly refocusing metrics. As a corollary, a contact Bott-Samelson type result by Frauenfelder, Labrousse, and Schlenk can be applied to Legendrian refocusing spacetimes to show that the Cauchy surface of a globally hyperbolic Legendrian refocusing spacetime of dimension at least $3$ is compact, that its fundamental group is finite, and that its universal cover has the integral cohomology ring of a compact rank one symmetric space (CROSS).

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Friedrich Bauermeister. 2026-07-05. Refocusing spacetimes need not be strongly refocusing. https://arxiv.org/abs/2605.21871

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