= Optical matrix of a null congruence
{title2=$\widehat B_{ab}=P_a{}^cP_b{}^d\nabla_dU_c$}
For affine null tangent $U$, choose an auxiliary null vector $N$ with $U\cdot N=-1$ and parallel transport it along the rays. The screen-space projector is $P_{ab}=g_{ab}+U_aN_b+N_aU_b$. The <optical matrix of a null congruence> describes evolution of screen-projected deviation vectors. Its trace is the null expansion, its symmetric trace-free part is the null shear, and its antisymmetric part is the null twist. In four dimensions $\widehat B=\theta P/2+\widehat\sigma+\widehat\omega$.
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