Null curve

A null curve has tangent $u$ satisfying $g(u,u)=0$. It represents the possible spacetime path of a light signal.

Its nonzero tangent is a null vector at every regular point; this distinguishes the curve from a single null direction.

A null geodesic is both a null curve and a geodesic. In geometric optics, light rays follow null geodesics.

In a flat two-dimensional Penrose diagram, a straight line tangent to a null vector; with radial metric tensor $-d{T}^2+d{X}^2$ it is $T-X=\mathrm{constant}$ or $T+X=\mathrm{constant}$. Such lines represent radial null geodesics after a conformal transformation.

A radial null geodesic in a spherically symmetric spacetime has zero angular momentum and fixed angular coordinates. Its projection is a null curve of the two-dimensional radial Lorentzian metric.