Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

Autor(es)

Mimoso, Jose P. ^{[1, 2]} ; Le Delliou, Morgan ^{[3, 1]} ; Mena, Filipe C. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Lisbon, Fac Ciencias, Ctr Astron & Astrofis, P-1769016 Lisbon - Portugal

^[2] Univ Lisbon, Fac Ciencias, Dept Fis, P-1769016 Lisbon - Portugal

^[3] Univ Sao Paulo, Inst Fis, Dept Fis Matemat, BR-05314970 Sao Paulo - Brazil

^[4] Univ Minho, Ctr Matemat, P-4710057 Braga - Portugal

• Tipo de documento: Artigo Científico
• Fonte: Physical Review D; v. 88, n. 4 AUG 1 2013.
• Citações Web of Science: 31

Resumo

We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a separating shell dividing expanding and collapsing regions. We resort to a 3 + 1 splitting and obtain gauge invariant conditions relating intrinsic spacetime quantities to properties of the matter source. We find that the separating shell is defined by a generalization of the Tolman-Oppenheimer-Volkoff equilibrium condition. The latter establishes a balance between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharp mass inside the separating shell and by the pressure fluxes. This defines a local equilibrium condition, but conveys also a nonlocal character given the definition of the Misner-Sharp mass. By the same token, it is also a generalized thermodynamical equation of state as usually interpreted for the perfect fluid case, which now has the novel feature of involving both the isotropic and the anisotropic stresses. We have cast the governing equations in terms of local, gauge invariant quantities that are revealing of the role played by the anisotropic pressures and inhomogeneous electric part of the Weyl tensor. We analyze a particular solution with dust and radiation that provides an illustration of our conditions. In addition, our gauge invariant formalism not only encompasses the cracking process from Herrera and co-workers but also reveals transparently the interplay and importance of the shear and of the anisotropic stresses. (AU)

• Processo FAPESP: 11/24089-5 - Astropartículas: cosmologia e formação de estruturas galácticas e aglomerados
• Beneficiário: Elcio Abdalla
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional