Brinkmann coordinates are a particular coordinate system for a spacetime belonging to the family of pp-wave metrics. They are named for Hans Brinkmann. In terms of these coordinates, the metric tensor can be written as

1. .

, the coordinate vector field dual to the covector, is a null vector field. Indeed, geometrically speaking, it is a null geodesic congruence with vanishing optical scalars. Physically speaking, it serves as the wave vector defining the direction of propagation for the pp-wave.

can be spacelike, null, or timelike at a given event in the spacetime are both spacelike vector can be thought of as a wavefront.

In discussions of exact solutions to the Einstein field equation, many authors fail to specify the intended range of the coordinate variables. Here we should take

to allow for the possibility that the pp-wave develops a null curvature singularity.

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