On the Conicality of Spacetimes
Abstract
The notion of conicality, recently introduced in [2403.00916], captures the extent to which the joint future of a finite set in spacetime uniquely determines the generating subset via its light cone structure. In the same paper it was mentioned that conicality holds for Minkowski spacetime of dimension 1+N with N≥ 2 and it has been conjectured that this property holds more generally. In this work, we show that neither homotopy with Minkowski space nor global hyperbolicity alone are sufficient for the spacetime to satisfy conicality. We then establish that causally simple, future cohesive spacetimes of dimension 1+N with N≥ 2 are conical. This class of spacetimes includes, in particular, TIP spacetimes, which can be understood as the timelike past of an observer. This is in line with the origin of causal modeling since the past of an observer is the natural domain for the description of experiments.
Related
BibTeX
@misc{ling2026conicality,
title = {{On the Conicality of Spacetimes}},
author = {Eric Ling and Claudio F. Paganini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.04643},
eprint = {2606.04643},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.04643},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Conicality of Spacetimes
AU - Eric Ling
AU - Claudio F. Paganini
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2606.04643
UR - https://arxiv.org/abs/2606.04643
AB - The notion of conicality, recently introduced in [2403.00916], captures the extent to which the joint future of a finite set in spacetime uniquely determines the generating subset via its light cone structure. In the same paper it was mentioned that conicality holds for Minkowski spacetime of dimension 1+N with N≥ 2 and it has been conjectured that this property holds more generally. In this work, we show that neither homotopy with Minkowski space nor global hyperbolicity alone are sufficient for the spacetime to satisfy conicality. We then establish that causally simple, future cohesive spacetimes of dimension 1+N with N≥ 2 are conical. This class of spacetimes includes, in particular, TIP spacetimes, which can be understood as the timelike past of an observer. This is in line with the origin of causal modeling since the past of an observer is the natural domain for the description of experiments.
ER -