  We systematically analyze the nonlinear partial differential equation that
determines the behaviour of a bounded radiating spherical mass in general
relativity. Four categories of solution are possible. These are identified in
terms of restrictions on the gravitational potentials. One category of solution
can be related to the horizon function transformation which was recently
introduced. A Lie symmetry analysis of the resulting Riccati equation shows
that several new classes of exact solutions are possible. The relationship
between the horizon function, Euclidean star models and other earlier
investigations is clarified.
