The impossibility of a simple derivation of the Schwarzschild metric

Abstract

The Schwarzschild metric, the general relativistic description of the space-time outside a spherical mass, has an extremely simple appearance. Because of this many attempts have been made to derive it by combining special relativity with concepts of Newtonian gravitation. It is shown here that such a derivation is impossible. A general discussion is given of the relationship of relativistic gravitation and its Newtonian limit with special emphasis on a particular non-Newtonian effect: spatial curvature.