Generalized proof of a mass-monopole criterion

A proof is presented demonstrating the general applicability of a formalism, developed in a previous paper, that is of theoretical significance to the Einstein-Infeld-Hoffmann approach to equations of motion in general relativity. This formalism, utilizing the scalar invariants of a vacuum gravitational field, allows one to determine the mass-monopole characteristics of a source perturbed by an arbitrary stress-energy distribution, by analyzing only its surrounding field. The proof utilizes the Regge-Wheeler-Zerilli method of tensor spherical harmonic decomposition of perturbations of a Schwarzschild background. It is concluded that a generalization of our formalism to a more complex source structure (as well as a proof that does not need to resort to any approximation procedures) must await a deeper understanding of the global properties of the eigenvalues of the Riemann curvature tensor.