Linearized General Relativity

Abstract

A complete theory of weak-field gravity is described: the linearized approximation. This is a form of first-order perturbation theory. The concept of a gauge transformation, as applied to the curvature tensor and the field equation, is explained, and it is shown how to reduce the field equation to a wave equation in the Lorenz gauge (under the linear approximation). Thus a huge variety of gravitational calculations become accessible.