Stability of an Ultra-Relativistic Blast Wave in an External Medium with   a Steep Power-Law Density Profile
  We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These accelerating solutions apply, for example, to the breakout of a gamma-ray burst outflow from the boundary of a massive star, as assumed in the popular collapsar model. We show that short wavelength perturbations may grow but only by a modest factor <~ 10. 
Xiaohu Wang, Abraham Loeb, Eli Waxman