Primordial magnetic seed field amplification by gravitational waves: comment on gr-qc/0503006

We consider the amplification of cosmological magnetic fields by gravitational waves as it was recently presented in [gr-qc/0503006]. That study confined to infinitely conductive environments, arguing that on spatially flat Friedmann backgrounds the gravito-magnetic interaction proceeds always as if the universe were a perfect conductor. We explain why this claim is not correct and then re-examine the Maxwell-Weyl coupling at the limit of ideal magnetohydrodynamics. We find that the scales of the main results of [gr-qc/0503006] were not properly assessed and that the incorrect scale assessment has compromised both the physical and the numerical results of the paper. This comment aims to clarify these issues on the one hand, while on the other it takes a closer look at the gauge-invariance and the nonlinearity of [gr-qc/0503006].