Separating expansion from contraction in spherically symmetric models
  with a perfect-fluid: Generalization of the Tolman-Oppenheimer-Volkoff
  condition and application to models with a cosmological constant
  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 Misner-Sharp mass
and to a function of the pressure that we introduce and that generalizes the
Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces
fulfilling those two conditions fit, locally, the requirements of a dividing
shell and we argue that cosmological initial conditions should allow its global
validity. We analyze the particular cases of the Lema\^itre-Tolman-Bondi dust
models with a cosmological constant as an example of a cold dark matter model
with a cosmological constant (\Lambda-CDM) and its generalization to contain a
central perfect-fluid core. These models provide simple, but physically
interesting illustrations of our results.
