Gullstrand–Painlevé Coordinates
Gullstrand–Painlevé (GP) coordinates were proposed by Paul Painlevé and Allvar Gullstrand in 1921. Similar to Schwarzschild coordinates, GP coordinates can be used in the Schwarzschild metric to describe the space-time physics on either side of the event horizon of a static black hole. However, Schwarzschild coordinates have a coordinate singularity at the event horizon, so are inconvenient for studying the behavior of objects crossing the event horizon.. GP coordinates were the first coordinates that could extend the analysis of space-time physics, such as the speed of particles and light, across the event horizon. The simplicity of the GP form makes it very useful for pedagogical purposes.
Read more about Gullstrand–Painlevé Coordinates: Derivation, Free-float Coordinates, Schwarzschild Coordinates, Shell Coordinates, Rain Coordinates, Gullstrand–Painlevé Coordinates, Speeds of Raindrop, Speeds of Light, A Rain Observer's View of The Universe