Evolution of radiating fluid spheres in general relativity

A general method to obtain models of nonstatic radiating fluid spheres is given. Through a certain parameter the models are continuously connected to static solutions of Einstein's equations. The procedure leads, with a minimum of additional hypothesis, to a system of three first-order differential equations for quantities evaluated at the surface of the sphere. An integration of this system allows one at once to obtain the profile of the physical variables inside the sphere. A criterion to predict the bounce of the surface appears in a natural way. As illustrations, we have integrated numerically the equations for two different models: The first is derived from the Schwarzschild interior solution and the second from Tolman's solution VI. In the first case bouncing of the surface is impossible but in the second model the bouncing may occur if certain conditions are satisfied.