Gravitational atoms beyond the test field limit: the case of Sgr A* and ultralight dark matter

Abstract We construct gravitational atoms including self-gravity, obtaining solutions of the Einstein–Klein–Gordon equations for a scalar field (SF) surrounding a non-rotating black hole (BH) in a quasi-stationary approximation. We resolve the region near the horizon as well as the far field one. Our results are relevant in a wide range of masses, from ultralight to MeV SFs and for BHs ranging from primordial to supermassive. For instance, the core of a galactic halo consistent with ultralight dark matter and a BH with a mass comparable to that of Sagittarius A* can be modeled. A density spike near the event horizon, although present, is negligible, contrasting with the prediction in Gondolo and Silk (1999 Phys. Rev. Lett. 83 1719–22) for cold dark matter.