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We construct a fully analytic, general relativistic, nonspinning black holebinary spacetime that approximately solves the vacuum Einstein equationseverywhere in space and time for black holes sufficiently well separated. Themetric is constructed by asymptotically matching perturbed Schwarzschildmetrics near each black hole to a two-body post-Newtonian metric far from them,and a two-body post-Minkowskian metric farther still. Asymptotic matching isdone without linearizing about a particular time slice, and thus it is validdynamically and for all times, provided the binary is sufficiently wellseparated. This approximate global metric can be used for long dynamicalevolutions of relativistic magnetohydrodynamical, circumbinary disks aroundinspiraling supermassive black holes to study a variety of phenomena.

Approximate black hole binary spacetime via asymptotic matching