  A class of nonstationary spacetimes is obtained by means of a conformal
transformation of the Schwarzschild metric, where the conformal factor $a(t)$
is an arbitrary function of the time coordinate only. We investigate several
situations including some where the final state is a central object with
constant mass. The metric is such that there is an initial big-bang type
singularity and the final state depends on the chosen conformal factor. The
Misner-Sharp mass is computed and a localized central object may be identified.
The trapping horizons, geodesic and causal structure of the resulting
spacetimes are investigated in detail. When $a(t)$ asymptotes to a constant in
a short enough time scale, the spacetime presents an event horizon and its
analytical extension reveals black-hole or white-hole regions. On the other
hand, when $a(t)$ is unbounded from above as in cosmological models, the
spacetime presents no event horizons and may present null singularities in the
future. The energy-momentum content and other properties of the respective
spacetimes are also investigated.
