Associated radius, energy and pressure of McVittie’s metric in its astrophysical application

Abstract

The McVittie metric is found to suffer inherent limitations. It is shown that the radius of the metric associated to the sphere has a correct asymptotic behaviour, ala Schwarzschild at the origin and ala Robertson- Walker when the the radial coordinater approaches infinity; but for intermediate values ofr 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, while the energy is negative 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.