Dynamics of Rarefaction Waves in General-Relativistic Collapsing Clouds
  Formation and evolution of general relativistic collapse inhomogeneity is investigated. It is shown that a rarefaction wave forms at initial collapse stages and propagates inside from the cloud boundary to its center. The focusing time of the rarefaction wave is found. In massive clouds, the rarefaction wave focusing time equals the free-fall time. The collapse of such clouds leads to black hole formation. In low-mass clouds, the rarefaction wave focusing time is less than the free-fall time. After focusing, the collapse of such clouds becomes fully inhomogeneous and can be sufficiently decelerated by the pressure gradient. 
A. G. Zhilkin