Metric structure and causality of lorentzian manifold

Abstract

We consider the topology of the BS causal completion, and show that it is not distorted in the causal direction. Using this result, we show that the causal completion with spacelike causal boundary in the sense of the BS construction satisfies the formal definition of the global hyperbolicity. We also consider the geodesic connectedness between the points of the completion and show that the causally related points can be connected by a corresponding geodesic.