Dynamics of Massive Shells Ejected in a Supernova Explosion
  An expanding shell is accelerated outward by radiation from the remnant star and slowed by ram pressure and accretion as it plows into the interstellar medium. We set up the general relativistic equations of motion for such a shell. In the non-relativistic limit, the reduce to the standard Ostriker-Gunn equations. Furthermore, it is shown that the motion equation can be integrated in general, reducing in this way the study of the dynamics of a shell to a set of four coupled first order differential equations, solvable up to quadrature 
D. Nunez and H. P. de Oliveira