  More than 300 supermassive black holes have been detected at redshifts larger
than 6, and they are abundant in the centers of local galaxies. Their formation
mechanisms, however, are still rather unconstrained. A possible origin of these
supermassive black holes could be through mergers in dense black hole clusters,
forming as a result of mass segregation within nuclear star clusters in the
center of galaxies. In this study, we present the first systematic
investigation of the evolution of such black hole clusters where the effect of
an external potential is taken into account. Such a potential could be the
result of gas inflows into the central region, for example as a result of
galaxy mergers. We show here that the efficiency for the formation of a massive
central object is mostly regulated by the ratio of cluster velocity dispersion
divided by the speed of light, potentially reaching efficiencies of 0.05-0.08
in realistic systems. Our results show that this scenario is potentially
feasible and may provide seeds black hole of at least 10^3 solar masses. We
conclude that the formation of seed black holes via this channel should be
taken into account in statistical assessments of the black hole population.
