The relativistic dynamics of a thin spherically symmetric radiating shell in the presence of a central body

An idealized spherically symmetric relativistic model of an exploding object is constructed within the framework of the theory of surface layers in general relativity. A Vaidya solution for a radially emitting star is matched through a spherical dust shell to a Schwarzschild solution. The (incomplete) equations of motion for the spherical dust shell and the radiation density of the Vaidya solution, as given by the matching conditions, are reduced to a first-order system, and a general analysis of the characteristics of the motion is given. This system of differential equations is completed by adding a relation between the unknowns which represent the simplest way to avoid an unphysical singularity in the motion. The results of a numerical integration of the equations are presented in two cases which may have some relationship to stellar explosions. A comparative set of results for other solutions is also given, and some possible generalizations of the model are pointed out.