  Formulating a perfect fluid filled spherically symmetric metric utilizing the
3+1 formalism for general relativity, we show that the metric coefficients are
completely determined by the mass-energy distribution, and its time rate of
change on an initial spacelike hypersurface. Rather than specifying
Schwarzschild coordinates for the exterior of the collapsing region, we let the
interior dictate the form of the solution in the exterior, and thus both
regions are found to be written in one coordinate patch. This not only
alleviates the need for complicated matching schemes at the interface, but also
finds a new coordinate system for the Schwarzschild spacetime expressed in
generalized Painleve-Gullstrand coordinates.
