Abstract
A model of a radiating star undergoing gravitational collapse is constructed by systematically studying both the boundary condition and equation of state for the first time. The resulting system of partial differential equations is analysed using Lie symmetries. The group analysis produces new classes of exact solutions with acceleration, expansion and shear in the presence of the cosmological constant. Known exact solutions are recovered as special cases of our solutions. In particular, we regain the Euclidean star model which is the relativistic version of the Newtonian star. The range of the equation of state parameters allows the solution to be interpreted as barotropic matter stars or dark energy stars. A particular case shows that the model is physically reasonable and the energy conditions are satisfied.
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