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

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.