The Causal Boundary construction has been in existence since 1972, as the most likely inherent boundary construction on a general strongly causal spacetime. But although there have been strong advances in topology and calculation on the Causal Boundary in recent decades, all studies heretofore have assumed a high degree of symmetry (spherically symmetric, static, and so on) or special algebraic construction (warped product, quotient by a group action, and the like). uyThe current investigation is the first to consider largely generic spacetimes.
We assume a foliation of the spacetime M by a family Q of observers--timelike curves--of finite lifetime. We then determine what physical observations (such as growth of rest-space metric) made by these observers will result in the Future Completeion of M--that is to say, M + Future Causal Boundary (FCB)--having the topology of (a, b] x Q, a manifold with boundary {b} x Q, with the FCB being entirely spacelike and occuring as the topologial boundary. This is modeled off of what happens in Interior Schwarzaschild.
We then determine some curvature conditions--integral conditions on sectional curvature of planes containing the observers-curves' velocity vectors--that guarantee that the metric on M extends continuously to the FCB, suggestive of a possible low-regularity extension of the spacetime. (This notably fails to happen in Interor Schwarzschild.)