Analysis of Dynamic Axial-Symmetric Shells

The aim of this work is to analyze the dynamical behavior of relativistic infinite axial-symmetric shells with flat interior and a radiation filled curved exterior spacetimes. It will be proven, by the use of conservation equations of Israel, that the given configuration does not let expansion or collapse of the shell which was proposed before, but rather the shell stays at constant radius. The case of null-collapse will also be considered in this work and it will be shown that the shell collapses to zero radius, and moreover, if cylindrical flatness is imposed a boundary layer is obtained still contrary to previous works.