Quasi-stationary solutions of self-gravitating scalar fields around black holes

TL;DR

This paper uses numerical relativity to demonstrate the existence and stability of long-lived, oscillating scalar field configurations around non-rotating black holes, supporting their potential role in dark matter halos.

Contribution

It provides the first long-term stable numerical simulations confirming quasi-stationary scalar field solutions around black holes in dynamical spacetimes.

Findings

Scalar fields form long-lived, oscillating configurations around black holes.

Simulations match linearized theory resonant frequencies.

Degeneracy in solutions affects test particle motion.

Abstract

Recent perturbative studies have shown the existence of long-lived, quasi-stationary configurations of scalar fields around black holes. In particular, such configurations have been found to survive for cosmological timescales, which is a requirement for viable dark matter halo models in galaxies based on such type of structures. In this paper we perform a series of numerical relativity simulations of dynamical non-rotating black holes surrounded by self-gravitating scalar fields. We solve numerically the coupled system of equations formed by the Einstein and the Klein-Gordon equations under the assumption of spherical symmetry using spherical coordinates. Our results confirm the existence of oscillating, long-lived, self-gravitating scalar fields configurations around non-rotating black holes in highly dynamical spacetimes with a rich scalar field environment. Our numerical simulations are long-term stable and allow for the extraction of the resonant frequencies to make a direct comparison with results obtained in the linearized regime. A byproduct of our simulations is the existence of a degeneracy in plausible long-lived solutions of Einstein equations that would induce the same motion of test particles, either with or without the existence of quasi-bound states.