Shear-free spherically symmetric spacetimes with an equation of state \(p=\alpha\rho\) (Q2741248)

In this paper authors study shear-free spherically symmetric spacetimes with barotropic equation of state in the \(\alpha\) - form \(p = \alpha \rho\) with \(\alpha\) being constant. They start with a spherically symmetric metric with all metric functions separable in time and radial coordinates and with energy-momentum tensor for fluid with heat flux. For the case with non-zero shear two coupled ordinary differential equations are obtained. These two equations are separable for shear-free spacetimes and all their shear-free solutions are presented. The authors apply these results for studying a model of a shear-free, spherical radiating star undergoing gravitational collapse. They match their interior solution with the Vaidya metric and consider the boundary region as a region with non-zero extent.