  We determine the causal structure of the McVittie spacetime for a
cosmological model with an asymmetric bounce. The analysis includes the
computation of trapping horizons, regular, trapped, and anti-trapped regions,
and the integration of the trajectories of radial null geodesics before,
during, and after the bounce. We find a trapped region since the beginning of
the contracting phase up to shortly before the bounce, thus showing the
existence of a black hole. When the universe reaches a certain minimum scale in
the contracting phase, the trapping horizons disappear and the central
singularity becomes naked. These results suggest that neither a contracting nor
an expanding universe can accommodate a black hole at all times.
