Dynamical instability for radiating anisotropic collapse

We study the role played by local anisotropy and radiation (in the free-streaming regime) in the onset of dynamical instabilities. In the case of anisotropy we find that, for Newtonian and post-Newtonian approximations, the relevant quantity is the anisotropy of the unperturbed fluid, and that small anisotropies may, in principle, drastically change the stability of the system. The influence of the free-streaming radiation upon stability appears to be qualitatively of the same type as that of radiative diffusion. Some speculations and prospective applications to astrophysical scenarios are presented