Abstract
We present a novel, few-body computational frame work designed to shed light on the likelihood of forming intermediate-mass (IM) and supermassive (SM) black holes (BHs) in nuclear star clusters (NSCs) through successive BH mergers, initiated with a single BH seed. Using observationally motivated NSC profiles, we find that the probability of an similar to 100 - M-circle dot BH to grow beyond similar to 1000 M-circle dot through successive mergers ranges from similar to 0.1 per cent in low-density, lo w-mass clusters to nearly 90 percent in high-mass, high-density clusters. Ho we ver, in the most massi ve NSCs, the gro wth time-scale can be very long (greater than or similar to 1 Gyr); vice versa, while growth is least likely in less massive NSCs, it is faster there, requiring as little as similar to 0 . 1 Gyr. The increased gravitational focusing in systems with lower velocity dispersions is the primary contributor to this behaviour. We find that there is a simple '7-strikes-and-you're-in' rule go v erning the growth of BHs: Our results suggest that if the seed survives 7-10 successive mergers without being ejected (primarily through gravitational wave recoil kicks), the growing BH will most likely remain in the cluster and will then undergo runaway, continuous growth all the way to the formation of an SMBH (under the simplifying assumption adopted here of a fixed background NSC). Furthermore, we find that rapid mergers enforce a dynamically mediated 'mass gap' between about 50 -300 M-circle dot in an NSC.