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
quilibrium 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. |