# The Effects of Self-Interaction on Constructing Relativistic Point Particles

## TL;DR

This paper develops a framework to analyze how self-interaction influences the initial data of point particles in General Relativity, providing rigorous proof of a mass vanishing claim and identifying geometric conditions affecting mass outcomes.

## Contribution

It introduces a novel framework for studying self-interaction effects on point particles and rigorously proves the mass vanishing claim by Arnowitt, Deser, and Misner.

## Key findings

- Proof of the mass vanishing claim for point sources
- Identification of geometric structures affecting mass
- Control of self-interaction effects through a scaling parameter

## Abstract

We introduce a framework for studying the effects of self-interaction on the construction of point particle initial data in General Relativity. Within this framework we rigorously prove the vanishing mass claim made by Arnowitt, Deser and Misner regarding point sources. We identify a geometric structure and a scaling parameter that allow one to determine, by controlling the effects of self-interaction, when one does or does not obtain a non-zero mass.