Kerr black holes with synchronised hair: an analytic model and dynamical formation

East and Pretorius (arXiv:1704.04791) have successfully evolved, using fully non-linear numerical simulations, the superradiant instability of the Kerr black hole (BH) triggered by a massive, complex vector field. Evolutions terminate in stationary states of a vector field condensate synchronised with a rotating BH horizon. We show these end points are fundamental states of Kerr BHs with synchronised Proca hair. Motivated by the "experimental data" from these simulations we suggest a universal (i.e. field-spin independent), analytic model for the subset of BHs with sychronised hair that possess a quasi-Kerr horizon, applicable in the weak hair regime. Comparing this model with fully non-linear numerical solutions of BHs with synchronised scalar or Proca hair, we show the model is accurate for hairy BHs that may emerge dynamically from superradiance, whose domain we identify.
Comment: 5+2 pages, 7 figures; data files and Mathematica notebooks can be found in this URL: http://gravitation.web.ua.pt/index.php?q=node/716