  We analyze the appearance of logarithmic terms at the critical sets of
Friedrich's cylinder representation of spatial infinity. It is shown that if
the radiation field vanishes at all orders at the critical sets no logarithmic
terms are produced in the formal expansions. Conversely, it is proved that,
under the additional hypothesis that the spacetime has constant (ADM) mass
aspect and vanishing dual (ADM) mass aspect, this condition is also necessary
for a spacetime to admit a smooth representation at the critical sets.
