In Minkowski spacetime, if we introduce spherical coordinates the metric becomes
$$\eta = dt^2-dr^2-r^2d\Omega^2$$
with $d\Omega^2$ the $S^2$ round metric. It is then common to introduce
$$u = t-r,\quad v=t+r$$
which sometimes are called retarded and advanced time, specially to study the infinity of spacetime. I've seem one analogous thing being done in Schwarzschild spacetime.
What we know about those is:
They are null. Hence their coordinate lines are paths that could be taken by photons.
If we pick the surfaces $u = u_0$ and $v = v_0$, these surfaces have $\partial_u$ and $\partial_v$ respectively as normals. The normals are lightlike, hence the surface is lightlike. Such surface doesn't qualify (as far as I know of course) as a "space at fixed time" locus differently from a surface $t = t_0$ for some timelike coordinate $t$.
The point is that in all these cases we have two null coordinates $u,v$, in other words, coordinates with null worldlines, which end up being called retarded and advanced time.
I can't see how these coordinates can get the name "time". They clearly doesn't seem to be "the time measured by some observer". So why are these coordinates referred as time coordinates, and why retarded/advanced anyway?