Interplay between Black Holes and Ultralight Dark Matter: Analytic Solutions

TL;DR

This paper analytically explores how ultralight scalar dark matter interacts with supermassive black holes, revealing effects like black hole hair, bound states, and soliton formation, with implications for accretion and gravitational responses.

Contribution

It provides new analytical solutions for scalar dark matter around black holes, including effects of boundary conditions, backreaction, and soliton formation, advancing understanding of dark matter-black hole interplay.

Findings

Scalar field decays as a power law, creating black hole hair.

Derived solutions for scalar profiles with rotating dark matter.

Calculated Love numbers and bound state spectra for scalar perturbations.

Abstract

Dark matter (DM) can consist of a scalar field so light that DM particles in the galactic halo are best described by classical waves. We investigate how these classical solutions are influenced by the presence of a non-rotating supermassive black hole at the center of the galaxy, using an analytical, albeit approximate, approach. Relying on this analytic control, we examine the consequences of imposing causal boundary conditions at the horizon, which are typically overlooked. First, we examine the scenario where the backreaction of dark matter can be neglected. The scalar field decays like a power law at large distances, thus endowing the black hole with "hair". We derive solutions for the field profile over a wide range of parameters, including cases with rotating dark matter. As a by-product, we extract the dynamical Love numbers for scalar perturbations. Next, we determine the spectrum of bound states and their behaviour. Finally, we incorporate the self-gravity of the scalar field, with a focus on the situation where dark matter forms a soliton (boson star) at the center of the galaxy. We derive an analytical expression for the soliton at every distance from the center. With a solution that remains applicable even at horizon scales, we can reliably compute the accretion rate of the black hole.