PreprintCC BY 4.0arXiv
Timelike ideal boundary of non-positively curved Lorentzian spaces
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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BibTeX
@misc{burgos2026timelike,
title = {{Timelike ideal boundary of non-positively curved Lorentzian spaces}},
author = {Saúl Burgos and Mauricio Che and Miguel Prados-Abad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.02496},
eprint = {2606.02496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.02496},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Timelike ideal boundary of non-positively curved Lorentzian spaces
AU - Saúl Burgos
AU - Mauricio Che
AU - Miguel Prados-Abad
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2606.02496
UR - https://arxiv.org/abs/2606.02496
AB - 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.
ER -