Separating expansion from contraction: generalized TOV condition, LTB models with pressure and $\Lambda$CDM

Morgan Le Delliou (1, 2) , Filipe C. Mena (3) , José Pedro Mimoso (2, 4)

1 IFT - Instituto de Física Teórica UAM/CSIC
2 CAAUL - Centro de Astronomia e Astrofísica da Universidade de Lisboa
3 CMAT - Centro de Matemática [Minho]
4 DFUL - Departamento de Fı́sica, Faculdade de Ciências [University of Lisbon]

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 $\Lambda$-CDM model) as an example of our results.

Mots clés: Cosmology; trapped matter surfaces; Tolman-Oppenheimer-Volkoff; General Relativity and Gravitation

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Physique des Hautes Energies - Théorie [hep-th]

Morgan Le Delliou, Filipe C. Mena, José Pedro Mimoso. Separating expansion from contraction: generalized TOV condition, LTB models with pressure and $\Lambda$CDM. 2009. ⟨hal-00429220⟩