Green's function in general relativity

Abstract: This report provides Green's functions (classical propagators) of gravitational fields appearing in general relativity. The existence of Green's function of the wave equation in curved space with an indefinite metric is ensured owing to the Hodge harmonic analysis. The analyticity of Green's function is determined intrinsically to keep a causality. This report proposed a novel definition of momentum space in curved space-time and the linearisation of the Einstein equation as a free field consistent with that of the Yang-Mills gauge field. The proposed linearisation does not utilize the weak-field approximation; thus, the method applies to highly caved space-time. We gave two examples of Green's function of gravitational fields: the plane wave solution and the Schwarzschild solution.