General matching of two spherically symmetric spacetimes

In this paper we show some very general results concerning the general matching of any two spherically symmetric spacetimes through a timelike hypersurface. We present a set of necessary conditions for this case which are very simple to use. As an important result, these conditions allow us to ascertain, by mere inspection of the conformal diagrams, which matchings are feasible in principle and which are not allowed. We shall illustrate these results by applying them to the general matching of Vaidya's radiating metric and the general flat Robertson-Walker spacetime with a linear equation of state, where all possible models are obtained. These particular models are relevant on their own as they describe interesting physical situations; some of them had not been considered hitherto.