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We have examined the invariant character of restrictions imposed on singularities or other sources of the gravitational fields in the Einstein-Infeld-Hoffmann theory of motion in general relativity. We have succeeded in providing a complete classification of sources that can occur in the linearized theory only, in terms of properties that are invariant under Lorentz and "gauge" transformations (the latter designation refers to linearized curvilinear coordinate transformations). Except for several explicitly known solutions, all solutions can be derived from a "supermetric" corresponding to the Hertz potential of electrodynamics. One method of classification is in terms of gauge-invariant integrals over spatial closed surfaces completely surrounding the particles. The motion of each source is determined by its own intrinsic angular momentum and dipole moment. The results do not depend on any particular assumed form of the stress-energy tensor of the sources.
Sachs et al. (Wed,) studied this question.