  We express Einstein's field equations for a spherically symmetric ball of
general fluid such that they are conducive to an initial value problem. We show
how the equations reduce to the Vaidya spacetime in a non-null coordinate
frame, simply by designating specific equations of state. Furthermore, this
reduces to the Schwarzschild spacetime when all matter variables vanish. We
then describe the formulation of an initial value problem, whereby a general
fluid ball with vacuum exterior is established on an initial spacelike slice.
As the system evolves, the fluid ball collapses and emanates null radiation
such that a region of Vaidya spacetime develops. Therefore, on any subsequent
spacelike slice there exists three regions; general fluid, Vaidya and
Schwarzschild, all expressed in a single coordinate patch with two
free-boundaries determined by the equations. This implies complicated matching
schemes are not required at the interfaces between the regions, instead, one
simply requires the matter variables tend to the appropriate equations of
state. We also show the reduction of the system of equations to the static
cases, and show staticity necessarily implies zero ``heat flux''. Furthermore,
the static equations include a generalization of the Tolman-Oppenheimer-Volkoff
equations for hydrostatic equilibrium to include anisotropic stresses in
general coordinates.
