Black hole hair from accretion of vector dark matter

Massive vector bosons, or dark photons, are a strong contender within the landscape of ultralight dark matter candidates. Motivated by a variety of string-compactification and beyond-the-Standard Model scenarios, massive vector fields have already been shown to exhibit a superradiant instability around Kerr black holes, which would allow them to settle into nontrivial "hairy" configurations in astrophysical situations. In this work, we consider hairy vector field solutions resulting not from superradiance, but rather from the accretion of particles from a cloud of non-relativistic vector dark matter filling the universe. Such a mechanism is compelling, as it is expected to provide hairy solutions for black holes of any mass and spin. For this initial investigation, we consider a Schwarzschild black hole with a single massive vector field, showing that hairy solutions exist for both the electric and the magnetic modes of the field. We discuss the structure of these solutions across the parameter space and explore their implications for black hole growth and detectability. This complements similar work done for massive scalar fields, for which both superradiant and accretion-sourced hair formation has been studied extensively.