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

We report on solutions to the Einstein field equations representing spherically symmetric, shear-free spacetimes with heat flux. The source matter for all of these spacetimes satisfies an equation of state of the barotropic form p = αρ where p and ρ are the pressure and density of the matter fluid while α is a constant. As an application, we model the collapse of a shear-free, radiating star which dissipates energy in the form of a radial 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 decrease as we move towards the boundary of this star. An interesting aspect of our solutions is that we can describe the formation of a semi-stable stellar configuration using our general relativistic solutions.