  We study the junction condition relating the pressure to the heat flux at the
boundary of a shearing and expanding spherically symmetric radiating star when
the fluid particles are travelling in geodesic motion. The Lie symmetry
generators that leave the junction condition invariant are identified and the
optimal system is generated. We use each element of the optimal system to
transform the partial differential equation to an ordinary differential
equation. New exact solutions, which are group invariant under the action of
Lie point infinitesimal symmetries, are found. We obtain families of traveling
wave solutions and self-similar solutions, amongst others. The gravitational
potentials are given in terms of elementary functions, and the line elements
can be given explicitly in all cases. We show that the Friedmann dust model is
regained as a special case, and we can connect our results to earlier
investigations.
