One can obtain the Schwarzschild and Robertson-Walker metrics from the McVittie metric in the exact limits of k = 0 , a ˙ ˙ ( t ) = 0 and μ μ ( t ) = 0 , respectively. In trying to describe the behavior of a mass particle in an expanding Universe, the original paper of McVittie a black hole spacetime with decreasing Schwarschild radius r s for an expanding surrounding cosmological spacetime. However, one can also interpret, in the limit of a small mass parameter μ μ ( t ) , a perturbed FLRW spacetime, with μ μ the Newtonian perturbation. Below we describe how to derive these analogies between the Schwarzschild and FLRW spacetimes from the McVittie metric.