Shear-free spherically symmetric spacetimes with an equation of state p = alpha rho

We report on solutions to the Einstein field equations representing spheric ally symmetric, shear-free spacetimes with heat flux. The source matter for all of these spacetimes satisfies an equation of state of the barotropic f orm p = alpha rho where p and rho are the pressure and density of the matte r fluid while alpha is a constant. As an application, we model the collapse of a shear-free, radiating star which dissipates energy in the form of a r adial heat flux. The heat flows from the hotter parts of the centre to the overlying cooler parts. The density, the pressure and the heat flux all dec rease as we move towards the boundary of this star. An interesting aspect o f our solutions is that we can describe the formation of a semi-stable stel lar configuration using our general relativistic solutions.