Abstract A method proposed by L. Herrera and collaborators in 1980 to study General Relativistic Spheres in the free streaming out is extended to handle a general radiating spheres. We have applied this method to study a specific scenario, where the luminosity profile is obtained for radially oscillating contracting spheres, and the evolution of the boundary surface is analyzed when pulsating profiles are provided. It is found that, in both cases the oscillatory frequency of the surface coincide with the frequency of the pulsating profile.