We investigate spherically symmetric solutions with pressure and
discuss the existence of a dividing shell separating expanding and
collapsing regions. We perform a 3+1 splitting and obtain gauge
invariant conditions relating not only the intrinsic spatial curvature
of the shells to the ADM mass, but also a function of the pressure which
we introduce and that generalises the Tolman-Oppenheimer-Volkoff
equilibrium condition. We also analyse particular cases like the
Lemaitre-Tolman dust models with a cosmological constant as an example
of a \Lambda-CDM model. These models provide simple, but physically
interesting illustrations of our results.
|