Boson Stars Hosting Black Holes

We study a system of a self-gravitating condensate, a boson star, formed from scalar ultra-light dark matter (ULDM), with a black hole hosted at its center. We numerically solve the equations of hydrostatic equilibrium in the non-relativistic limit, consistently incorporating the gravitational potential of the black hole, to obtain all possible configurations of this BS-BH system for different boson star masses, interaction types, and black hole masses. We also propose an analytic expression for the density profile and compare it with the numerical results, finding good agreement for attractive interactions and for a finite range of mass ratios between the black hole and boson star. Finally, considering the inspiral of this BS-BH system with a second, smaller black hole, we study the dephasing of gravitational waves due to the presence of the ULDM environment. A Fisher matrix analysis reveals the regions of parameter space of the ULDM mass and self-coupling that future gravitational-wave observatories such as LISA can probe.