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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.

We investigate the formation of a locally naked singularity in the collapse of radiation shells in an expanding Vaidya-deSitter background. This is achieved by considering the behaviour of non-spacelike and radial geodesics originating at the singularity. A specific condition is determined for the existence of radially outgoing, null geodesics originating at the singularity which, when this condition is satisfied, becomes locally naked. This condition turns out to be the same as that in the collapse of radiation shells in an asymptotically flat background. Therefore, we have, at least for the case considered here, established that the asymptotic flatness of the spacetime is not essential for the development of a locally naked singularity. Our result then unequivocally supports the view that no special role be given to asymptotic observers (or, for that matter, any set of observers) in the formulation of the Cosmic Censorship Hypothesis.