Conjectures on the Relations of Linking and Causality in Causally Simple Spacetimes

Abstract: We formulate the generalization of the Legendrian Low conjecture of Natario and Tod (proved by Nemirovski and myself before) to the case of causally simple spacetimes. We prove a weakened version of the corresponding statement. In all known examples, a causally simple spacetime $(X, g)$ can be conformally embedded as an open set into some globally hyperbolic $(\widetilde X, \widetilde g)$ and the space of light rays in $(X, g)$ is an open submanifold of the space of light rays in $(\widetilde X, \widetilde g)$. If this is always the case, this provides an approach to solving the conjectures relating causality and linking in causally simples spacetimes.