Dynamics of a spherical object of uniform density in an expanding
  universe
  We present Newtonian and fully general-relativistic solutions for the
evolution of a spherical region of uniform interior density \rho_i(t), embedded
in a background of uniform exterior density \rho_e(t). In both regions, the
fluid is assumed to support pressure. In general, the expansion rates of the
two regions, expressed in terms of interior and exterior Hubble parameters
H_i(t) and H_e(t), respectively, are independent. We consider in detail two
special cases: an object with a static boundary, H_i(t)=0; and an object whose
internal Hubble parameter matches that of the background, H_i(t)=H_e(t). In the
latter case, we also obtain fully general-relativistic expressions for the
force required to keep a test particle at rest inside the object, and that
required to keep a test particle on the moving boundary. We also derive a
generalised form of the Oppenheimer-Volkov equation, valid for general
time-dependent spherically-symmetric systems, which may be of interest in its
own right.
