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In the 1990's Christodoulou introduced an idealized fluid model intended tocapture some of the features of the gravitational collapse of a massive star toform a neutron star or a black hole. This was the two-phase model introduced in'Self-gravitating relativistic fluids: a two phase model', Arch. Rational Mech.Anal. 130, 343-400 (1995). The present work deals with the formation of a freephase boundary in the phase transition from hard to soft in this model. In thiscase the phase boundary has corners at the null points, the points whichseparate the timelike and spacelike components of the interface between the twophases. We prove existence and uniqueness of a free phase boundary. Also thelocal form of the shock near the null point is established.

Self-Gravitating Relativistic Fluids: The Formation of a Free Phase Boundary in the Phase Transition from Hard to Soft