Separating expansion from collapse and generalizing TOV condition in spherically symmetric models with pressure, with $\Lambda$-CDM examples

par Morgan Le Delliou (UAM Madrid)

jeudi 11 févr. 2010, 14:00 → 15:00 Europe/Paris

Auditorium M. Vivargent (LAPTH)

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 and that generalises the Tolman-Oppenheimer-Volkov equilibrium condition. We also analyse particular cases like the Lemaitre-Tolman dust models with a cosmological constant as an example of a $\Lambda$-CDM model. These models provide simple, but physically interesting illustrations of our results. For the \Lambda$-CDM example, we also analyse the asymptotic behaviour of the trapped matter shells using a Generalised Lemaître-Tolman-Bondi (GLTB) description with general initial conditions, and the only constraints of having spatially asymptotic cosmological expansion, initial Hubble-type flow, simultaneous bang time, and finite initial density distribution. We discuss the effects of shell crossing and use a dynamical analysis and topological description of the local trapped matter shells to explore global properties of the models. We find a splitting of the separating properties into two globally defined shells, from which only one separating shell always survives within the above hypotheses, for spatially expanding models.

Slides LeDelliou.pdf