Using highly-accurate $N$-body simulations, we explore the evolution of multiple massive black holes (hereafter, MBHs) in a primordial galaxy that is composed of stars and MBHs. The evolution is pursed with a fourth-order Hermite scheme, where not only three-body interaction of MBHs but also dynamical friction by stars are incorporated. Initially, ten MBHs with equal mass of $10^7M_\odot$ are set in a host galaxy with $10^{11}M_\odot$. It is found that 4 - 6 MBHs merge successively within 1 Gyr, emitting gravitational wave radiation. The key process for the successive merger of MBHs is the dynamical friction by field stars, which enhances three-body interactions of MBHs when they enter the central regions of the galaxy. The heaviest MBH always composes a close binary at the galactic center, which shrinks owing to the angular momentum transfer by the third MBH and eventually merges. The angular momentum transfer by the third MBH is due to the sling-shot mechanism. We find that the secular Kozai mechanism does not work for a binary to merge if we include the relativistic pericenter shift. The simulations show that a multiple MBH system can produce a heavier MBH at the galactic center purely through $N$-body process. This merger path can be of great significance for the growth of MBHs in a primordial galaxy. The merger of multiple MBHs may be a potential source of gravitational waves for the Laser Interferometer Space Antenna (LISA) and pulsar timing.
GW231123: Likely a product of successive mergers from $\sim 10 $ stellar-mass black holes
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（暗物质和空间天文重点实验室，中国科学院紫金山天文台）；Department of Physics, University of Florida（佛罗里达大学物理系）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）
The Dragon-II simulations -- III. Compact binary mergers in clusters with up to 1 million stars: mass, spin, eccentricity, merger rate and pair instability supernovae rate
基于 Dragon-II 的 19 个 N 体星团模拟，研究致密双星并合的质量、偏心率、并合率及不稳定对超新星率，揭示原初与动力学并合的差异，并给出多信使探测前景。
