Extensions of the Taub and NUT spaces and extensions of their tangent bundles

Abstract

A system of extensions of the Taub space and the NUT space with the topology due to Misner is constructed having the property: for each incomplete geodesic in these space-times, there is one and only one extension from the system into which the geodesic smoothly continues. Next, the notion of hypermanifold is introduced which is a generalization of tangent bundle of a space-time, and an untrivial hypermanifold is constructed that contains the tangent bundles of the Taub and NUT spaces as proper submanifolds, and within which almost all geodesics are complete. Locally, the hypermanifolds do not yield anything new, but they provide much broader choice of global properties than any four-dimensional space-time manifold.