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We discuss the existence of a dividing shell separating expanding andcollapsing regions in spherically symmetric solutions with pressure. We obtaingauge invariant conditions relating not only the intrinsic spatial curvature ofthe shells to the ADM mass, but also a function of the pressure which weintroduce that generalises the Tolman-Oppenheimer-Volkoff equilibriumcondition, in the framework of a 3+1 spacetime splitting. We consider theparticular case of a Lema\^itre-Tolman-Bondi dust models with a cosmologicalconstant (a $\Lambda$-CDM model) as an example of our results.

Separating expansion from contraction: generalized TOV condition, LTB models with pressure and $\Lambda$CDM