In order to study the type of collapse mentioned in the title, we introduce a physically meaningful object, called the horizon function. It directly enters the expressions for many of the stellar characteristics. The main junction equation, which governs the collapse, transforms into a Riccati equation with simple coefficients for the horizon function. We integrate this equation in the geodesic case. The same is done in the general case when one or another of the coefficients vanish. It is shown how to build classes of star models in this formulation of the problem and simple solutions are given.
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