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Theory and observations suggest that single-star evolution is not able toproduce black holes (BHs) with masses in the range $3-5M_{\odot}$ and above$\sim 45M_{\odot}$, referred to as the lower mass gap (LMG) and the upper masgap (UMG), respectively. However, it is possible to form BHs in these gapsthrough merger of compact objects in dense clusters, e.g. the LMG and the UMGcan be populated through binary neutron star- and BBH mergers, respectively.This implies that if binary mergers are observed in gravitational waves (GWs)with at least one mass gap object, then either clusters are effective inassembling binary mergers, or our single-star models have to be revised.Understanding how effective clusters are at populating both mass gaps havetherefore major implications for both stellar- and GW astrophysics. In thispaper we present a systematic study on how efficient stellar clusters are atpopulating both mass gaps through in-cluster GW mergers. For this, we derive aset of closed form relations for describing the evolution of compact objectbinaries undergoing dynamical interactions and GW merger inside their cluster.By considering both static and time evolving populations, we find in particularthat globular clusters are clearly inefficient at populating the LMG incontrast to the UMG. We further describe how these results relate to thecharacteristic mass, time, and length scales associated with the problem.

Populating the Black Hole Mass Gaps In Stellar Clusters: General Relations and Upper Limits