  Current theoretical models predict a mass gap with a dearth of stellar black
holes (BHs) between roughly $50\,M_\odot$ and $100\,M_\odot$, while, above the
range accessible through massive star evolution, intermediate-mass BHs (IMBHs)
still remain elusive. Repeated mergers of binary BHs, detectable via
gravitational wave emission with the current LIGO/Virgo/Kagra interferometers
and future detectors such as LISA or the Einstein Telescope, can form both
mass-gap BHs and IMBHs. Here we explore the possibility that mass-gap BHs and
IMBHs are born as a result of successive BH mergers in dense star clusters. In
particular, nuclear star clusters at the centers of galaxies have deep enough
potential wells to retain most of the BH merger products after they receive
significant recoil kicks due to anisotropic emission of gravitational
radiation. We show that a massive stellar BH seed can easily grow to $\sim 10^3
- 10^4\,M_\odot$ as a result of repeated mergers with other smaller BHs. We
find that lowering the cluster metallicity leads to larger final BH masses. We
also show that the growing BH spin tends to decrease in magnitude with the
number of mergers, so that a negative correlation exists between final mass and
spin of the resulting IMBHs. Assumptions about the birth spins of stellar BHs
affect our results significantly, with low birth spins leading to the
production of a larger population of massive BHs.
