We study a self-gravitating ultralight dark matter condensate (a boson star) hosting a central black hole, in the nonrelativistic limit, which we refer to as a boson star black hole (BS-BH) system. We numerically solve the equations of hydrostatic equilibrium, 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 dark matter environment. A Fisher matrix analysis reveals the regions of parameter space of the dark matter mass and self-coupling that future gravitational wave observatories such as LISA can probe.

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• Dark matter
• Gravitation
• Gravitational waves