Conformally Embedded Spacetimes and the Space of Null Geodesics

摘要

It is shown that the space of null geodesics of a causally simple spacetime is Hausdorff if it admits an open conformal embedding into a globally hyperbolic spacetime. This provides an obstruction to conformal embeddings of causally simple spacetimes into globally hyperbolic ones irrespective of curvature conditions. Examples of causally simple spacetimes are given not conformally embeddable into globally hyperbolic ones.