Eddington–Finkelstein coordinates

Summary

Eddington–Finkelstein coordinates are coordinates on the Schwarzschild spacetime adapted to radial light rays. They replace the Schwarzschild time $t$ by a null coordinate, so that the metric stays regular across the horizon $r = 2m$. They show that the singularity of the Schwarzschild metric at $r = 2m$ comes from the coordinates and not from the geometry. They are the simplest way to see the interior of a black hole.