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arXiv · 2606.02496

Timelike ideal boundary of non-positively curved Lorentzian spaces

Saúl Burgos·Mauricio Che·Miguel Prados-Abad
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Abstract

We introduce the notion of timelike ideal boundary of a Lorentzian length space as the set of asymptotic classes of future or past-directed timelike geodesic rays, a construction complementary to the causal boundary in the sense of Geroch-Kronheimer-Penrose and akin to the concept of ideal boundary of a metric space. We endow such a timelike ideal boundary with a natural cone topology and an angular metric, and establish upper curvature bounds for the resulting metric space. Finally, we consider generalized cones as a model and study the relation between the timelike ideal boundary and both the metric ideal boundary of the fiber and the asymptotic behaviour of the warping function.

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Saúl Burgos, Mauricio Che, Miguel Prados-Abad. 2026-06-01. Timelike ideal boundary of non-positively curved Lorentzian spaces. https://arxiv.org/abs/2606.02496

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