Abstract
The future causal boundary on a spacetime serves to explicate the causal behavior of the spacetime at future infinity. The purely causal nature of this boundary has a categorically universal nature, the category being that of chronological sets. There is an associated topology with any chronological set, replicating the appropriate topology for a spacetime. Adding the future causal boundary (and using this topology) provides a quasi-compactification. The boundary for a product spacetime \(M \times \mathbb L^1\) can be detailed in terms of the Riemannian factor M.
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Harris, S.G. Boundaries on spacetimes: causality, topology, and group actions. Geom Dedicata 126, 255–274 (2007). https://doi.org/10.1007/s10711-007-9168-2
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DOI: https://doi.org/10.1007/s10711-007-9168-2