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Abstract

The propagation equations for small perturbations of a background gravitational field satisfying the EINSTEIN equations are considered. For the perturbation potential the covariantly generalized EINSTEIN-HILBERT gauge is chosen. With the aid of the method used in [10], bitensor GREEN's functions for the propagation equations in a weak vacuum field are given explicitly. The tail term is obtained to be an integral of the first-order RIEMANN curvature tensor. As an application of the formulae, GREEN's functions for perturbations of the SCHWARZSCHILD metric are calculated to first order in the mass parameter.