Search

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., Comment: 17pp, 9 figures, accepted by PRD

5 pages, 4 figures.-- PACS: 98.80.-k, 98.80.Cq, 98.80.Jk, 95.30.Sf , 04.40.Nr, 04.20.Jb, We discuss the existence of a dividing shell separating expanding and collapsing regions in spherically symmetric solutions with pressure. We 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 that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition, in the framework of a 3+1 spacetime splitting. We consider the particular case of a Lemaître-Tolman- Bondi dust models with a cosmological constant (a L-CDM model) as an example of our results., The work of MLeD is supported by CSIC (Spain) under the contract JAEDoc072, with partial support from CICYT project FPA2006-05807, at the IFT, Universidad Autonoma de Madrid, Spain, and was also supported by FCT (Portugal) under the grant SFRH/BD/16630/2004, at the CFTC, Lisbon University, Portugal. Financial support from the Foundation of the University of Lisbon and the Portuguese Foundation for Science and Technology (FCT) under contract POCTI/ISFL/2/618 is also gratefully acknowledged. FCM is supported by CMAT, Univ. Minho, and FCT project PTDC/MAT/108921/2008.

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 that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition. We consider the particular case of a Lema\^itre-Tolman dust models with a cosmological constant (a $\Lambda$-CDM model) as an example of our results., Comment: 4pp, 1fig, AIP Conference: Proc. XXXI Spanish Relat. Meeting, ERE08, Salamanca, Spain, 15-19 Sept., 2008 Septembre, Salamanca, Espagne