  We prove nonlinear stability of compactly supported expanding star-solutions
of the mass-critical gravitational Euler-Poisson system. These special
solutions were discovered by Goldreich and Weber in 1980. The expanding rate of
such solutions can be either self-similar or non-self-similar (linear), and we
treat both types. An important outcome of our stability results is the
existence of a new class of global-in-time radially symmetric solutions, which
are not homogeneous and therefore not encompassed by the existing works. Using
Lagrangian coordinates we reformulate the associated free-boundary problem as a
degenerate quasilinear wave equation on a compact spatial domain. The problem
is mass-critical with respect to an invariant rescaling and the analysis is
carried out in similarity variables.
