Dynamical black hole in a bouncing universe
  We analyze the causal structure of McVittie spacetime for a classical
bouncing cosmological model. In particular, we compute the trapping horizons of
the metric and integrate the trajectories of radial null geodesics before,
during, and after the bounce takes place. In the contracting phase up to the
occurrence of the bounce, a dynamical black hole is present. When the universe
reaches a certain minimum scale, the trapping horizons disappear and the black
hole ceases to exist. After the bounce, the central weak singularity becomes
naked. In the expanding phase, for large positive values of the cosmic time,
the behaviour of null geodesics indicates that the solution contains a black
hole. These results suggest that neither a contracting nor an expanding
universe can accommodate a black hole at all times.
