Schwarzschild and Birkhoff a la Weyl

We provide a simple derivation of the Schwarzschild solution in general relativity based on an approach by Weyl, but generalized to include Birkhoff’s theorem. This theorem states that the Schwarzschild mass must be constant in time. Our procedure is illustrated by a parallel derivation of the Coulomb field and the constancy of the electric charge in electrodynamics. We also explain the basis of Birkhoff’s theorem and note that even the original Weyl approach can be used to illuminate the special role played by the Schwarzschild coordinates.