The interaction of outgoing and ingoing spherically symmetric null fluids

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Abstract
Using similarity methods, the Einstein field equations coupled to two oppositely directed null fluids for a spherically symmetric space–time are reduced to an autonomous system of three ordinary differential equations. The space of solutions is studied in some detail and solutions are found that represent: (i) the backscattering of an initially outgoing thick null fluid shell in a background gravitational field with a central naked singularity, (ii) the formation of strong space–time singularities by the interaction of thick null fluid shells, (iii) the interaction of a core of null radiation with an incoming shell of null fluid, and (iv) cosmological models of Kantowski–Sachs type with initial and final singularities clothed by apparent horizons.