  A systematic analysis of the junction condition, relating the radial pressure
with the heat flow in a shear-free relativistic radiating star, is undertaken.
This is a highly nonlinear partial differential equation in general. We obtain
the Lie point symmetries that leave the boundary condition invariant. Using a
linear combination of the symmetries, we transform the junction condition into
ordinary differential equations. We present several new exact solutions to the
junction condition. In each case we can identify the exact solution with a Lie
point generator. Some of the solutions obtained satisfy the linear barotropic
equation of state. As a special case we regain conformally flat models which
were found previously. Our analysis highlights the interplay between Lie
algebras, nonlinear differential equations and application to relativistic
astrophysics.
