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

摘要

Recent perturbative studies have shown the existence of long-lived,quasi-stationary configurations of scalar fields around black holes. Inparticular, such configurations have been found to survive for cosmologicaltimescales, which is a requirement for viable dark matter halo models ingalaxies based on such type of structures. In this paper we perform a series ofnumerical relativity simulations of dynamical non-rotating black holessurrounded by self-gravitating scalar fields. We solve numerically the coupledsystem of equations formed by the Einstein and the Klein-Gordon equations underthe assumption of spherical symmetry using spherical coordinates. Our resultsconfirm the existence of oscillating, long-lived, self-gravitating scalarfields configurations around non-rotating black holes in highly dynamicalspacetimes with a rich scalar field environment. Our numerical simulations arelong-term stable and allow for the extraction of the resonant frequencies tomake a direct comparison with results obtained in the linearized regime. Abyproduct of our simulations is the existence of a degeneracy in plausiblelong-lived solutions of Einstein equations that would induce the same motion oftest particles, either with or without the existence of quasi-bound states.