River of Light is a sword form. It is used as a draw-cut, usually ment to unsheath the sword and strike in the same motion. Eamon Valda used this form against Galadedrid Damodred during thier Trial Beneath the Light, albeit his sword was already out of its scabbard. Had Galad not quickly countered with Rain in High Wind, Valda would have sheared off one of Galad's arms.
There is a similar technique in the Japanese sword-art of Iaido.