Green's functions for a static charge in a weakly-curved spacetime
We present our calculation of the Green's function for a static scalar and electric charge in a weakly-curved spacetime. We find that to leading order the scalar Green's function reduces to the Green's function for the Poisson equation in Euclidean space. We also calculate the next order correction in the scalar Green's function. We also present the recurrence relation for the Green's function of static electric charge. The calculations that we present here are needed to modernize the self-force expressions in a weakly-curved spacetime.