PoMiN: A Post-Minkowskian $N$-Body Solver

TL;DR

PoMiN is a lightweight, general relativistic N-body simulation code based on the post-Minkowskian approximation, capable of handling many particles with validated accuracy.

Contribution

It introduces PoMiN, a novel N-body solver incorporating first-order relativistic effects and scalable to many particles, with detailed validation methods.

Findings

PoMiN accurately reproduces analytical solutions.

The code demonstrates good convergence and conservation properties.

PoMiN scales as O(N^2) for arbitrary particle numbers.

Abstract

In this paper, we introduce PoMiN, a lightweight $N$-body code based on the post-Minkowskian $N$-body Hamiltonian of Ledvinka et. al., which includes general relativistic effects up to first order in Newton's constant $G$, and all orders in the speed of light $c$. PoMiN is written in C and uses a fourth-order Runge-Kutta integration scheme. PoMiN has also been written to handle an arbitrary number of particles (both massive and massless), with a computational complexity that scales as $O(N^2)$. We describe the methods we used to simplify and organize the Hamiltonian, and the tests we performed (convergence, conservation, and analytical comparison tests) to validate the code.