On superposition of relativistic point-sources

TL;DR

This paper proposes an extended framework for superposing relativistic point-sources in general relativity, recovering known metrics and connecting to Newtonian gravity, addressing the challenge posed by the theory's non-linearity.

Contribution

It introduces a novel extension of an existing framework to enable a superposition principle for relativistic point-sources, aligning with classical and known relativistic solutions.

Findings

Recover Brill-Lindquist metrics as a limit

Propose a continuous superposition of point-sources

Bridge relativistic and Newtonian gravity principles

Abstract

The non-linearity of general relativity makes it at least difficult if not impossible to view a relativistic cloud of matter as being made up of point-source constituents. Perhaps the most delicate issue to circumnavigate is the inherent lack of the classical notion of superposition. Even if one were to believe that the recent framework developed by the first and the third author leads to an appropriate interpretation of the phrase initial data for a point-source, there is prima facie no reason to believe that it lends itself to a principle of superposition. In this paper we propose an extension of said framework which serves as a de-facto superposition of point-sources and which recovers Brill-Lindquist metrics in the limit. We also show that our proposal can be seen as a continuous extension of the classical superposition principle of Newtonian gravity. This paper fits within a larger program of representing relativistic clouds of matter as cumulative effects of point-sources.