Uniqueness of maximal spacetime boundaries (Q6630487)

The paper under review studies the uniqueness of extension problem of spacetimes. The authors consider a class of extensions in which the extended manifold is a topological manifold with boundary. Moreover, their extended manifolds can be seen as the result of attaching to the original spacetime \(M\) the limit points of inextendible incomplete (in \(M\)) time-like geodesics, i.e, every point in the boundary should be the endpoint of a future directed timelike geodesis. They also demand that the manifold topology of the extension can be reconstructed in a very precise way from the time-like geodesics of the original spacetime. The main result of the paper is that non-uniqueness of the extension can arise essentially only from time-like geodesics getting arbitrarily close to each other.