Relativistic scalar dark matter drag forces on a black hole binary

Dark matter around black holes can induce drag forces through dynamical friction and accretion, potentially affecting the orbital evolution and gravitational wave emission of binary systems. While dynamical friction from scalar field dark matter has been studied in the relativistic regime for single black holes, the case of a binary black hole (BBH) has remained unexplored. As a first step, we present a series of two-dimensional general-relativistic simulations of BBH in a wind tunnel for an asymptotically homogeneous scalar field background. We extract the drag forces, torque, mass and charge accretion acting on the binary, and analyze their dependence on the binary separation, velocity and the scalar field parameters. We find that the binary's drag is not a simple superposition of two isolated black holes; the presence of a companion modifies the gravitational wake and yields significant nonlinearities. This additional force and torque can (in principle) modify the inspiral and induce a dephasing of the gravitational wave signal.