  Criteria which a space-time must satisfy to represent a point mass embedded
in an open Robertson--Walker (RW) universe are given. It is shown that
McVittie's solution in the case $k=0$ satisfies these criteria, but does not in
the case $k=-1$. Existence of a solution for the case $k=-1$ is proven and its
representation in terms of an elliptic integral is given. The following
properties of this and McVittie's $k=0$ solution are studied; uniqueness,
behaviour at future null infinity, recovery of the RW and Schwarzschild limits,
compliance with energy conditions and the occurence of singularities. Existence
of solutions representing more general spherical objects embedded in a RW
universe is also proven.
