Collapsing Layers on Schwarzschild-Lemaitre Geodesics

We discuss Israel layers collapsing inward from rest at infinity along Schwarzschild-Lemaitre geodesics. The dynamics of the collapsing layer and its equation of state are developed. There is a general equation of state which is approximately polytropic in the limit of very low pressure. The equation of state establishes a new limit on the stress-density ratio.