Dynamical instability and the expansion-free condition

Details Dynamical instability and the expansion-free condition Dynamical instability and the expansion-free condition

2010-10-07

arxiv.org/abs/1010.1518v2

Gen. Rel. Grav. 44, 1143, (2012)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages Revtex. Some changes in the text to match the version accepted in Gen. Rel. Grav

Scientific paper

10.1007/s10714-012-1331-x

We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index $\Gamma_1$, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.

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