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Separating cosmology from astrophysics: generalized TOV condition in LTB models with pressure

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.
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