  McVittie's solution of Einstein's field equations, representing a point mass
embedded into an isotropic universe, possesses a scalar curvature singularity
at proper radius $R=2m$. The singularity is space-like and precedes, in the
expanding case, all other events in the space-time. It is shown here that this
singularity is gravitationally weak, and the possible structure of the region
$R\leq 2m$ is investigated. A characterization of this solution which does not
involve asymptotics is given.
