Perturbed Characteristic Functions: Application to the Linearized Gravitational Field

The first-order perturbation induced by the first-order perturbation of a given Lagrangian in its associated characteristic function V is given by a simple integral along the unperturbed extremals. This result is applied to the world characteristic of the linearized gravitational field. Various specialized situations are considered. For example, to obtain V(1) in the quasi-Newtonian approximation one merely needs to evaluate a three-dimensional volume integral over the product of the energy density and a type of two-point Green's function.