  A representation of spatial infinity based in the properties of conformal
geodesics is used to obtain asymptotic expansions of the gravitational field
near the region where null infinity touches spatial infinity. These expansions
show that generic time symmetric initial data with an analytic conformal metric
at spatial infinity will give rise to developments with a certain type of
logarithmic singularities at the points where null infinity and spatial
infinity meet. These logarithmic singularities produce a non-smooth null
infinity. The sources of the logarithmic singularities are traced back down to
the initial data. It is shown that is the parts of the initial data responsible
for the non-regular behaviour of the solutions are not present, then the
initial data is static to a certain order. On the basis of these results it is
conjectured that the only time symmetric data sets with developments having a
smooth null infinity are those which are static in a neighbourhood of infinity.
This conjecture generalises a previous conjecture regarding time symmetric,
conformally flat data. The relation of these conjectures to Penrose's proposal
for the description of the asymptotic gravitational field of isolated bodies is
discussed.
