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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

J. P. Mimoso, M. Le Delliou, F. C. Mena

Abstract
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 Lemaītre-Tolman-Bondi dust models with a cosmological constant as an example of a cold dark matter model with a cosmological constant(Lambda-CDM model) and its generalization to contain a central perfect-fluid core. These models provide simple but physically interesting illustrations of our results.

Keywords
Cosmology - Mathematical: and: relativistic: aspects: of: cosmology - Relativity: and: gravitation - Einstein-Maxwell: spacetimes - spacetimes: with: fluids: radiation: or: classical: fields

Physical Review D
Volume 81, Issue 12, Page 123514_1
2010 June

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Instituto de AstrofĆ­sica e CiĆŖncias do EspaƧo Universidade do Porto Faculdade de Ciências da Universidade de Lisboa
FundaĆ§Ć£o para a CiĆŖncia e a Tecnologia COMPETE 2020 PORTUGAL 2020 UniĆ£o Europeia