Schwarzschild and Birkhoff a la Weyl

TL;DR

This paper offers a straightforward derivation of the Schwarzschild solution and Birkhoff's theorem in General Relativity, extending Weyl's approach and illustrating the method with an analogous derivation in electrodynamics.

Contribution

It introduces a simplified, unified derivation of key solutions and theorems in General Relativity and electrodynamics, emphasizing their Hamiltonian foundations.

Findings

Derivation of Schwarzschild solution using Weyl's approach

Proof of Birkhoff's theorem on mass constancy

Parallel derivation of Coulomb field and charge constancy

Abstract

We provide a simple derivation of the Schwarzschild solution in General Relativity, generalizing an early approach by Weyl, to include Birkhoff's theorem: constancy of the mass; its deeper, Hamiltonian, basis is also given. Our procedure is illustrated by a parallel derivation of the Coulomb field and constancy of electric charge, in electrodynamics.