On the Motion of Shells in General Relativity

We use Lanczos equations to analyze the motionof shells in the gravitational field of a sphericallysymmetric central body. A first integral of Israel'smatching conditions is used to show that the motion of the shell depends on the equation of stateof the shell matter. In particular, the case of abarotropic equation of state is analyzed. The questionof how the type of motion determines the equation of state for the matter of the shell is alsoinvestigated.