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

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.

arXiv comment11 pages w/ 3 figures. Revised to match published version

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• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• The Limited Accuracy of Linearized Gravity
• The hierarchical three-body problem at $\mathcal{O}(G^2)$