Boundaries on spacetimes: causality, topology, and group actions

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.