For irrotational dust the shear tensor is consistently diagonalizable with its covariant time derivative: $\sigma_{ ab}=0=\dot{ \sigma}_{ ab},\; a\neq b$, if and only if the divergence of the magnetic part of the Weyl tensor vanishes: $div~H = 0$. We show here that in that case, the consistency of the Ricci constraints requires that the magnetic part of the Weyl tensor itself vanishes: $H_{ ab}=0$.
Categories: gr-qc