Fold bifurcations in shearing radiative collapse

A simple form of the gravitational field for a radiating relativistic star with nonzero shear is studied. The junction conditions at the surface of the star reduce to an autonomous nonlinear first order differential equation of the Riccati type: it admits exact solutions and is amenable to a phase plane analysis. We can determine the temporal evolution and asymptotic behaviour of the radiating star including shear, charge and the cosmological constant. The presence of shear leads to behaviour which is distinct from shear-free models and fold bifurcations arise; the model collapses from an initial static configuration or a superdense cold star forms. The areal distance plays a central role in the asymptotic analysis and there is an interplay with the charge and the cosmological constant.