  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.
