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

${\displaystyle ds^{2}=H(u,x,y)du^{2}+2dudv+dx^{2}+dy^{2}}$

Here, ${\displaystyle \partial _{v}}$, the coordinate vector field dual to the covector field ${\displaystyle dv}$, 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.

The coordinate vector field ${\displaystyle \partial _{u}}$ can be spacelike, null, or timelike at a given event in the spacetime, depending upon the sign of ${\displaystyle H(u,x,y)}$ at that event.

The coordinate vector fields ${\displaystyle \partial _{x},\partial _{y}}$ are both spacelike vector fields. The surfaces ${\displaystyle u=u_{0},v=v_{0}}$ can be thought of as defining wavefronts. In the special case of Baldwin/Jeffery plane waves, these are each isometric to an ordinary euclidean plane; in general, they might have nonzero Gaussian curvature.