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

Details 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 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

2009-10-30

arxiv.org/abs/0910.5755v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17pp, 9 figures, accepted by PRD

Scientific paper

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.

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