2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200109We consider non-rotating geodesic perfect fluid spacetimes which are purely radiative in the sense that the gravitational field satisfies the covariant transverse conditions div H = div E = 0. We show that when the shear tensor S is degenerate, H, E and S necessarily commute and hence the resulting spacetimes are hypersurface homogeneous of Bianchi class A (modulo some purely electric exceptions).8 pages, references added, typos corrected, simplified some algebraic manipulationsGeneral Relativity and Quantum Cosmologytext