Spherically symmetric models: separating expansion from contraction in models with anisotropic pressures

Abstract

We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We find that the dividing shell is defined by a relation between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharpe mass inside the separating shell and by the pressure fluxes. This balance is a generalization of the Tolman-Oppenheimer- Volkoff equilibrium condition which defines a local equilibrium condition, but conveys also a non- local character given the definition of the Misner-Sharpe mass. We present a particular solution with dust and radiation that provides an illustration of our results.

4pp Towards New Paradigms: Proceeding Of The Spanish Relativity Meeting 2011. AIP Conference Proceedings, Volume 1458, pp. 487-490 (2012). Published in AIP Conf.Proc. 1458 (2011) 487-490