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The non-linearity of general relativity makes it at least difficult if notimpossible to view a relativistic cloud of matter as being made up ofpoint-source constituents. Perhaps the most delicate issue to circumnavigate isthe inherent lack of the classical notion of superposition. Even if one were tobelieve that the recent framework developed by the first and the third authorleads to an appropriate interpretation of the phrase initial data for apoint-source, there is prima facie no reason to believe that it lends itself toa principle of superposition. In this paper we propose an extension of saidframework which serves as a de-facto superposition of point-sources and whichrecovers Brill-Lindquist metrics in the limit. We also show that our proposalcan be seen as a continuous extension of the classical superposition principleof Newtonian gravity. This paper fits within a larger program of representingrelativistic clouds of matter as cumulative effects of point-sources.

On superposition of relativistic point-sources