Making sense of the bizarre behavior of horizons in the McVittie spacetime

The bizarre behavior of the apparent (black hole and cosmological) horizons of the McVittie spacetime is discussed using, as an analogy, the Schwarzschild-de Si tier-Kottier spacetime (which is a special case of McVittie anyway). Fora dust-dominated "background" universe, a black hole cannot exist at early times because its (apparent) horizon would be larger than the cosmological (apparent) horizon. A phantom-dominated background universe causes this situation, and the horizon behavior, to be time-reversed.