I"m trying to understand the exact/technical link between the Eikonal equation and a double-null form of the metric (if such a direct link even exists). R. Wald, in his "General Relativity", doesn't say anything about it.
A function $f$ satisfies (per definition) the Eikonal equation if
$g(\nabla f,\nabla f)=0$
i.e. the gradient field $\nabla f$ is a null vector field.
On the other hand, a metric $g$ has double-null coordinates $(u,v)$ if $g=h+F\dot dudv$ (i.e. no $du^{2}$ and $dv^{2}$ terms appear).
I was wondering if there is a direct link between this function $f$ and the metric double null form?
Thank you for any hints.
This post imported from StackExchange MathOverflow at 2015-12-17 17:23 (UTC), posted by SE-user GregVoit