Paper detail

Quasistationary solutions of scalar fields around accreting black holes

Massive scalar fields can form long-lived configurations around black holes. These configurations, dubbed quasi-bound states, have been studied both in the linear and nonlinear regimes. In this paper we show that quasi-bound states can form in a dynamical scenario in which the mass of the black hole grows significantly due to the capture of infalling matter. We solve the Klein-Gordon equation numerically in spherical symmetry, mimicking the evolution of the spacetime through a sequence of analytic Schwarzschild black hole solutions of increasing mass. It is found that the frequency of oscillation of the quasi-bound states decreases as the mass of the black hole increases. In addition, accretion leads to a significative increase of the exponential decay of the scalar field energy due to the presence of terms of order higher than linear in the exponent. We compare the black hole mass growth rates used in our study with estimates from observational surveys and extrapolate our results to values of the scalar field masses consistent with models that propose scalar fields as dark matter in the universe. We show that even for unrealistically large mass accretion rates, quasi-bound states around accreting black holes can survive for cosmological timescales. Our results provide further support to the intriguing possibility of the existence of dark matter halos based on (ultra-light) scalar fields surrounding supermassive black holes in galactic centers.