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We investigate spherically symmetric solutions with pressure and discuss theexistence of a dividing shell separating expanding and collapsing regions. Weperform a 3+1 splitting and obtain gauge invariant conditions relating not onlythe intrinsic spatial curvature of the shells to the ADM mass, but also afunction of the pressure which we introduce that generalises theTolman-Oppenheimer-Volkoff equilibrium condition. We consider the particularcase of a Lema\^itre-Tolman dust models with a cosmological constant (a$\Lambda$-CDM model) as an example of our results.

Separating expansion from contraction and generalizing TOV condition in spherically symmetric models with pressure