The bizarre behavior 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 behavior, to be time-reversed.
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Faraoni et al. (2012) studied this question.
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