2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201117We consider irrotational dust spacetimes in the full non-linear regime which are "purely radiative" in the sense that the gravitational field satisfies the covariant transverse conditions div(H) = div(E) = 0. Within this family we show that the Bianchi class A spatially homogeneous dust models are uniquely characterised by the condition that $H$ is diagonal in the shear-eigenframe.6 pages, ERE 2006 conference, minor correctionsGeneral Relativity and Quantum Cosmologytext