RIT Logo with Text
Approximate Black Hole Binary Spacetime via Asymptotic Matching
By Bruno C. Mundim, Hiroyuki Nakano, Nicolás Yunes, Manuela Campanelli, Scott C. Noble, Yosef Zlochower
Published in Physical Review D 89, 084008 (Tuesday, April 8, 2014)


We construct a fully-analytic, general relativistic, non-spinning black hole binary spacetime that approximately solves the vacuum Einstein equations everywhere in space and time for black holes sufficiently well-separated. The metric is constructed by asymptotically matching perturbed Schwarzschild metrics 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 is done without linearizing about a particular time slice, and thus it is valid dynamically and for all times, provided the binary is sufficiently well-separated. This approximate global metric can be used for long dynamical evolutions of relativistic magnetohydrodynamical, circumbinary disks around inspiraling supermassive black holes to study a variety of phenomena.