  We generalize Birkhoff's Theorem in the following fashion. We find necessary
and sufficient conditions for any spherically symmetric space-time to be static
in terms of the eigenvalues of the stress-energy tensor. In particular, we
generalize the Tolman-Oppenheimer-Volkoff equation and prove that Birkhoff's
theorem holds under the weaker hypothesis of no pressure (with respect to an
appropriate frame.) We provide equations that show how the coefficients of the
metric relate to the eigenvalues of the stress-energy tensor. These involve
integrals that are simple functions of those eigenvalues. We also determine
among all static spherically symmetric space-times those that are
asymptotically flat. A few examples are presented taking advantage of the
results. The calculations are done by viewing the space-times as warped
products and the computations are done using Cartan's moving frames approach.
