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

Abstract: The bizarre behaviour of the apparent (black hole and cosmological) horizons of the McVittie spacetime is discussed using, as an analogy, the Schwarzschild-de Sitter-Kottler spacetime (which is a special case of McVittie anyway). For a 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 behaviour, to be time-reversed.