Separating the Sources of Chaos in the Relativistic 3 Body Problem

TL;DR

This study investigates whether chaos and other dynamic features in the relativistic 3 body problem are primarily due to relativistic effects or if they already exist in Newtonian physics, highlighting the dominant role of field propagation time.

Contribution

The paper introduces bespoke simulation code to distinguish the effects of relativistic corrections from Newtonian dynamics in the 3 body problem, emphasizing the significance of field propagation time.

Findings

Field propagation time impacts system behavior more than Post Newtonian corrections.

Angular momentum transfer from the binary system influences the test mass.

Preliminary results suggest new insights into accretion disc dynamics in binary systems.

Abstract

The dynamics of the Restricted 3 Body Problem in the Post Newtonian context have been, and continue to be, studied extensively and a number of characteristics such as ejections of bodies from the system, precession of orbits, chaotic trajectories and collisions are investigated and classified. In this paper, I examine the extent to which these characteristics are attributable to Relativistic causes (more correctly Post Newtonian approximations of Relativistic causes) or more prosaically whether these characteristics already exist in the Newtonian case and whether these or other effects would also be caused by the time of propagation of the field, the impact of which is less well covered in the literature. In this project I have written bespoke code for the simulations and present the results in a methodical way showing many of the steps in the process. In the Appendices, I discuss the technical challenges of constructing, testing and calibrating the code, so that other non-experts in the field can reproduce the code and results and build on the work that I have done. Although the work done here must be considered preliminary, results suggest that the impact of the field propagation time on the behaviour of the test mass in the restricted 3 body problem outweighs the impact of the Post Newtonian corrections, in particular due to a transfer of angular momentum from the binary system to the test mass, and this effect may therefore be of interests to those studying accretion discs of binary systems.