Generalizing Birkhoff

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