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We study the long term dynamical evolution of stellar mass black holes (BHs)at the Galactic center (GC) and put constraints on their number and centralmass distribution. Models of the GC are considered that have not yet achieved asteady state under the influence of random gravitational encounters. Contraryto some recent claims that mass-segregation can rapidly rebuild a density cuspin the stars, we find that time scales associated with cusp regrowth are longerthan the Hubble time. These results cast doubts on standard models thatpostulate high densities of BHs near the GC and motivate studies that startfrom initial conditions which correspond to well-defined physical models. Forthe first time, we consider the distribution of BHs in a dissipationlessformation model for the Milky Way nuclear cluster (NC), in which massivestellar clusters merge in the GC to form a nucleus. We simulate the successiveinspiral of massive clusters containing an inner dense cluster of BHs. Thepre-existing mass segregation is not completely erased as the clusters aredisrupted by the massive black hole tidal field. As a result, after 12 inspiralevents a NC forms in which the BHs have higher central densities than thestars. After evolving the model for 5-10 Gyr, the BHs do form a steep centralcusp, while the stellar distribution maintains properties that resemble thoseof the Milky Way NC. Finally, we investigate the effect of BH perturbations onthe motion of the GC S-stars, as a means of constraining the number of theperturbers. We find that reproducing the S-star orbital distribution requires>~1000 BHs within 0.1 pc of Sgr A*. A dissipationless formation scenario forthe Milky Way NC is consistent with this lower limit and therefore couldreconcile the need for high central densities of BHs (to explain the orbits ofthe S-stars), with the missing-cusp problem of the GC giant star population.

On the distribution of stellar remnants around massive black holes: slow mass segregation, star cluster inspirals and correlated orbits