Irrotational dust with divH=0

For irrotational dust the shear tensor is consistently diagonalizable with its covariant time derivative: ${\mathrm{\sigma }}_{\mathit{a}\mathit{b}}$=0=σ${\mathrm{̇}}_{\mathit{a}\mathit{b}}$, a≠b, if and only if the divergence of the magnetic part of the Weyl tensor vanishes: divH=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: ${\mathit{H}}_{\mathit{a}\mathit{b}}$=0. © 1996 The American Physical Society.