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

TL;DR

This paper develops models of gravitational atoms including self-gravity effects, solving Einstein-Klein-Gordon equations around black holes, with implications for ultralight dark matter and supermassive black holes like Sgr A*.

Contribution

It introduces solutions that incorporate self-gravity in gravitational atom models, extending beyond the test field approximation for a wide range of black hole and scalar field masses.

Findings

Negligible density spike near the horizon in realistic scenarios

Models applicable to ultralight dark matter and supermassive black holes

Solutions include near-horizon and far-field regions

Abstract

We construct gravitational atoms including self-gravity, obtaining solutions of the Einstein-Klein-Gordon equations for a scalar field surrounding a non-rotating black hole in a quasi-stationary approximation. We resolve the region near the horizon as well as the far field region. Our results are relevant in a wide range of masses, from ultralight to MeV scalar fields and for black holes ranging from primordial to supermassive. For instance, a system with a scalar field consistent with ultralight dark matter and a black hole 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 [P. Gondolo and Silk, Phys. Rev. Lett., 83:1719-1722, 1999] for cold dark matter.