# Oppenheimer-Snyder Collapse

### From GRwiki

Oppenheimer-Snyder collapse is the gravitational collapse of a uniform ball of dust. The initial areal radius of the ball is and the ADM mass is . The Oppenheimer-Snyder solution is a piecing together of two other exact line element solutions at the surface boundary of a uniform spherical ball of uncharged dust. The external solution is the Schwarzschild solution. Internal to the matter the solution is the closed Fiedmann line element

"To model a pressureless ball" the and are then parameterized in terms of a timelike coordinate according to

where matching boundary conditions we relate to the initial Schwarzschild radial coordinate radius of the matter by

and have

The Schwarzschild radial coordinate radius of the matter as a function of our timelike coordinate parameter is

And the Schwarzschild time evaluated at the surface can be related to our timelike coordinate parameter by

and the Kerr-Schild coordinate velocity of the surface with respect to the remote observer is finally