Dynamical instability for shearing viscous collapse

We study the role played by the shear and shearing viscosity in the onset of dynamical instabilities. For both the Newtonian and the relativistic regimes, the shearing viscosity decreases the instability of the fluid. The corrections due to the shear, which appear only in the post-Newtonian approximation, decrease the range of values of the ‘ratio of specific heats’ for which the system is unstable. This result is the consequence of the fact that the collapse with shear proceeds faster than the corresponding shear-free collapse. Under otherwise identical conditions, therefore, the material of the collapsing sphere with shear should be softer than the material of the shear-free collapsing sphere.