Embedding a Black Hole in AN Isotropic Universe

In this contribution, we discuss the problem of finding an exact solution of Einstein's field equations representing a spherical black hole, i.e. the Schwarzschild solution, embedded in an isotropic background. The results quoted have appeared in (Nolan '98, '99a, '99b). One aim of such a study is to facilitate the discussion of the effect of the observed cosmological expansion on local systems, e.g. the solar system. Our starting point is the observation that the Einstein-Straus model (Einstein and Straus '45) does not provide a suitable solution to this problem; see (Senovilla + Vera '97, Mars '98). McVittie's solution (McVittie '33) purports to represent such a space-time. We ask: (i) Is this the case? (ii) Is it a suitable test-bed for the question of cosmic expansion vs. local dynamics? ...