Brinkmann coordinates are a particular coordinate system for a spacetime belonging to the family of pp-wave metrics. They are named for . In terms of these coordinates, the metric tensor can be written as where , the coordinate vector field dual to the covector field , is a null vector field. Indeed, geometrically speaking, it is a with vanishing optical scalars. Physically speaking, it serves as the wave vector defining the direction of propagation for the pp-wave. to allow for the possibility that the pp-wave develops a .