Outgoing null oblate spheroidal coordinates
= Outgoing null oblate spheroidal coordinates
Starting from the <Minkowski metric> in <oblate spheroidal coordinates>, set $u=t-r$, $R=r$, and choose an azimuth $\varphi$ satisfying
$$
d\varphi=d\phi-\frac{a}{R^2+a^2}dR.
$$
Then
$$
ds^2=-du^2-2\,du\,dR
+2a\sin^2\theta\,dR\,d\varphi
+(R^2+a^2\cos^2\theta)d\theta^2
+(R^2+a^2)\sin^2\theta\,d\varphi^2,
$$
so the coordinate vector $\partial_R$ is null.