Accelerating $N$-body simulation of self-gravitating systems with limited first-order post-Newtonian approximation

TL;DR

This paper presents a GPU-accelerated $N$-body simulation code for self-gravitating systems using a limited first-order post-Newtonian approximation, enabling efficient analysis of star dynamics around massive black holes.

Contribution

The study develops a GPU-accelerated $N$-body simulation code incorporating a limited first-order post-Newtonian approximation for self-gravitating systems.

Findings

GPU acceleration achieves tens of times speed-up for $N \,\simeq\, 10^4$ objects

Code effectively models star behavior around massive black holes

Simulation demonstrates feasibility of post-Newtonian approximation in large systems

Abstract

In this study, an $N$-body simulation code was developed for self-gravitating systems with a limited first-order post-Newtonian approximation. The code was applied to a special case in which the system consists of one massive object and many low-mass objects. Therefore, the behavior of stars around the massive black hole could be analyzed. A graphics processing unit (GPU) was used to accelerate the code execution, and it could be accelerated by several tens of times compared to a single-core CPU for $N \simeq 10^4$ objects.