  Recently we studied the effects of information carrying waves propagating
through isotropic cosmologies. By information carrying we mean that the waves
have an arbitrary dependence on a function. We found that the waves introduce
shear and anisotropic stress into the universe. We then constructed explicit
examples of pure gravity wave perturbations for which the presence of this
anisotropic stress is essential and the null hypersurfaces playing the role of
the histories of the wave-fronts in the background space-time are shear-free.
Motivated by this result we now prove that these two properties are true for
all information carrying waves in isotropic cosmologies.
