We evolve for the first time in full general relativity a small, collisional $N$-body black hole (BH) cluster of arbitrary total mass $M$. The bound cluster is initially compact (radius $R/M\sim 10$), stable, and consists of 25 equal-mass, nonspinning BHs. The dynamical interactions of compact objects in $N$-body clusters is of great interest for the formation of BHs in the upper mass gap as well as intermediate and supermassive BHs. These are potential sources of gravitational waves that may be detected by both current and future observatories. Unlike previous $N$-body Newtonian and post-Newtonian simulations, no “subgrid physics” is required to handle collisions and mergers. We can therefore confirm in full general relativity several predictions from these simulations and analytic estimates: the runaway growth of a large BH via repeated mergers; spindown of the central BH with increasing captures; the ejection of a BH with a large asymptotic velocity due to a several-body interaction; and a regime where mergers occur primarily via direct collisions on highly eccentric orbits instead of quasicircular inspirals. We extract the gravitational wave signal and find it has several distinct features associated with the compact cluster regime. Our results suggest the signal is sufficiently loud that next generation observatories would likely be able to detect similar events across most of the observable universe. This work is a preliminary proof-of-principle study that we hope will open up a new arena for numerical relativity and the study of $N$-body compact systems.

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• General relativity
• Gravitational wave sources
• Astronomical black holes
• Globular clusters
• Primordial black holes
• Numerical relativity