Physical limitations of McVittie metric

The McVittie metric is found to suffer inherent limitations. It is known that the radius of the metric associated to the sphere has a eorrect asymptotic behaviour, à la Schwarzschild at the origin and à la Robertson-Walker whenthe radial coordinate r approaches infinity; but for intermediate values of r and acceptable mass values of the Schwarzschild singularity, minimum and maximum are present, both disappearing solely for mass values larger than the universe radius. Furthermore the pressure is infinite at the Schwarzschild radius, whil the energy is negativ for particular values of negative universe curvature. An alternative interpretation, reverse to the purposes of the McVittie solution, hints at a metric comparable to an internal solution.