= Screen space of a null congruence
{title2=$k^\perp/\operatorname{span}\{k\}$}
= Screen space
{synonym}
The <screen space of a null congruence> describes directions transverse to a bundle of lightlike trajectories. For a nonzero <null vector> $k$, its orthogonal space $k^\perp$ contains $k$ itself, so the induced metric there is degenerate. Removing this physically longitudinal direction gives the <quotient vector space>
$$
k^\perp/\operatorname{span}\{k\}.
$$
In four-dimensional <Lorentzian manifold> it is two-dimensional and has a positive-definite induced metric under the $(-,+,+,+)$ convention.
Choosing an auxiliary null direction lets one represent this quotient by an ordinary transverse plane and a screen projector. That choice is useful for calculation, but the quotient is the intrinsic object. The <optical matrix of a null congruence> then describes expansion, shear and rotation of transverse separations rather than a spurious change along the rays themselves.
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