A CURVATURE-BASED DERIVATION OF THE SCHWARZSCHILD METRIC

We give a derivation of Schwarzschild and other spherically symmetric solutions in general relativity which starts by computing the curvatur es directly from Einstein's equations and Bianchi identities, and then derives the metric. This transforms the ''plausibility'' argument for the Schwarzschild metric given by Berry in his book Principles of Cos mology and Gravitation into a complete derivation, which puts the stre ss from the beginning on the curvatures, the quantities which actually correspond to the gravitational field. (C) 1997 American Association of Physics Teachers.