The Legendrian Low conjecture for nonrefocussing globally hyperbolic spacetimes

Let $(X^{m+1},g)$ be a globally hyperbolic spacetime with $m\geq 2$. Two points are causally related when one lies in the causal future or causal past of the other, and their skies are Legendrian submanifolds of the space of light rays of $(X,g)$. The Legendrian Low conjecture for nonrefocussing spacetimes. Causal relation of two points is equivalent to Legendrian linking of their skies, provided that one cannot put a globally hyperbolic and refocussing metric on $X$. The claim generalizes the known low-dimensional cases described in the source and is intended as a higher-dimensional extension; it remains open.