  Theory and observations suggest that single-star evolution is not able to
produce 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 mas
gap (UMG), respectively. However, it is possible to form BHs in these gaps
through merger of compact objects in dense clusters, e.g. the LMG and the UMG
can 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 in
assembling binary mergers, or our single-star models have to be revised.
Understanding how effective clusters are at populating both mass gaps have
therefore major implications for both stellar- and GW astrophysics. In this
paper we present a systematic study on how efficient stellar clusters are at
populating both mass gaps through in-cluster GW mergers. For this, we derive a
set of closed form relations for describing the evolution of compact object
binaries undergoing dynamical interactions and GW merger inside their cluster.
By considering both static and time evolving populations, we find in particular
that globular clusters are clearly inefficient at populating the LMG in
contrast to the UMG. We further describe how these results relate to the
characteristic mass, time, and length scales associated with the problem.
