Accretion-driven growth of massive vector hair around Schwarzschild black holes*

Dark photons, described by ultralight spin-1 fields coupled weakly to standard model matter, are a dark matter candidate of particular interest for gravitational physics. Appearing frequently in a variety of string-compactification and beyond-the-Standard Model scenarios, these fields can, for masses of ~10^-20 - 10^-10 eV, form steady-state condensates or "hair" around astrophysical black holes. In this work, we consider the growth of massive vector hair around a black hole via accretion, modeled by endowing the field with nontrivial boundary conditions at spatial infinity. Unlike superradiance, this accretion mechanism allows for hair growth in both spinning and non-spinning spacetimes. We present both analytical and numerical results, focusing for now on the steady-state structure of these condensates around Schwarzschild black holes. This complements similar work done for massive scalar fields, for which both superradiant and accretion-sourced hair formation has been studied extensively. Such condensates, if sufficiently common, could be detectable both through direct emission of gravitational waves as they decay and through their effect on binary mergers. Understanding their phenomenology is thus essential for the future of gravitational-wave astrophysics.