  We construct an approximate metric that represents the spacetime of spinning
binary black holes (BBH) approaching merger. We build the metric as an
analytical superposition of two Kerr metrics in harmonic coordinates, where we
transform each black hole term with time-dependent boosts describing an
inspiral trajectory. The velocities and trajectories of the boost are obtained
by solving the post-Newtonian (PN) equations of motion at 3.5 PN order. We
analyze the spacetime scalars of the new metric and we show that it is an
accurate approximation of Einstein's field equations in vacuum for a BBH system
in the inspiral regime. Furthermore, to prove the effectiveness of our
approach, we test the metric in the context of a 3D general relativistic
magneto-hydrodynamical (GRMHD) simulation of accreting mini-disks around the
black holes. We compare our results with a previous well-tested spacetime
construction based on the asymptotic matching method. We conclude that our new
spacetime is well-suited for long-term GRMHD simulations of spinning binary
black holes on their way to the merger.
