Spherically symmetric models with pressure: separating expansion from contraction and generalizing TOV condition
Résumé
We investigate spherically symmetric perfect fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a $3+1$ splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the ADM mass and to a function of the pressure which we introduce and that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition. We analyse the particular cases of the Lema\^{\i}tre-Tolman-Bondi dust models with a cosmological constant as an example of a $\Lambda$-CDM model and its generalization to contain a central perfect fluid core. These models provide simple, but physically interesting illustrations of our results.
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