  Theoretical modeling of massive stars predicts a gap in the black hole (BH)
mass function above $\sim 40-50\,M_{\odot}$ for BHs formed through single star
evolution, arising from (pulsational) pair-instability supernovae. However, in
dense star clusters, dynamical channels may exist that allow construction of
BHs with masses in excess of those allowed from single star evolution. The
detection of BHs in this so-called "upper-mass gap" would provide strong
evidence for the dynamical processing of BHs prior to their eventual merger.
Here, we explore in detail the formation of BHs with masses within or above the
pair-instability gap through collisions of young massive stars in dense star
clusters. We run a suite of 68 independent cluster simulations, exploring a
variety of physical assumptions pertaining to growth through stellar
collisions, including primordial cluster mass segregation and the efficiency of
envelope stripping during collisions. We find that as many as $\sim20\%$ of all
BH progenitors undergo one or more collisions prior to stellar collapse and up
to $\sim1\%$ of all BHs reside within or above the pair-instability gap through
the effects of these collisions. We show that these BHs readily go on to merge
with other BHs in the cluster, creating a population of massive BH mergers at a
rate that may compete with the "multiple-generation" merger channel described
in other analyses. This has clear relevance for the formation of very massive
BH binaries as recently detected by LIGO/Virgo in GW190521. Finally, we
describe how stellar collisions in clusters may provide a unique pathway to
pair-instability supernovae and briefly discuss the expected rate of these
events and other electromagnetic transients.
