Schwarzschild and Birkhoff a la Weyl
Abstract
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.
 Publication:

American Journal of Physics
 Pub Date:
 March 2005
 DOI:
 10.1119/1.1830505
 arXiv:
 arXiv:grqc/0408067
 Bibcode:
 2005AmJPh..73..261D
 Keywords:

 01.40.d;
 04.20.Jb;
 03.50.De;
 41.20.Cv;
 Education;
 Exact solutions;
 Classical electromagnetism Maxwell equations;
 Electrostatics;
 Poisson and Laplace equations boundaryvalue problems;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 8 pages. Clarifying remarks and historic references added, accepted for publication in Amer. J. Phys