Radial null trajectories in ingoing Eddington-Finkelstein coordinates
= Radial null trajectories in ingoing Eddington-Finkelstein coordinates
Radial null curves comprise the ingoing family $v=\text{constant}$ and the outgoing family
$$
\frac{dr}{dv}=\frac12\left(1-\frac{2M}{r}\right).
$$
Outside the horizon the outgoing family moves to larger $r$; inside it both future-directed families move to smaller $r$.