Oblate spheroidal coordinates

With parameter $a\ge 0$, oblate spheroidal coordinates on Euclidean three-space areWriting $\Sigma =r^2+a^2{\cos }^2\theta$ and $\Delta =r^2+a^2$, their spatial line element is

Starting from the Minkowski metric in oblate spheroidal coordinates, set $u=t-r$, $R=r$, and choose an azimuth $\phi$ satisfyingThenso the coordinate vector ${\partial }_R$ is null.