Dynamics of crossing cosmological shells

Abstract

The crossing of three dust shells is considered as a simplified model for shell crossing during the spherically symmetric collapse of dust which interacts only gravitationally. The formalism is developed in both Schwarzschild and Kruskal coordinates. This represents a highly inhomogeneous closed universe in which the matter is distributed on three thin shells only. We followed their motion with multiple crossings and we found how the number of crossings depends on the initial data.