Spinning, Precessing, Black Hole Binary Spacetime via Asymptotic Matching

Abstract

We briefly discuss a method to construct a global, analytic, approximate spacetime for precessing, spinning binary black holes. The spacetime construction is broken into three parts: the inner zones are the spacetimes close to each black hole, and are approximated by perturbed Kerr solutions; the near zone is far from the two black holes, and described by the post-Newtonian metric; and finally the wave (far) zone, where retardation effects need to be taken into account, is well modeled by the post-Minkowskian metric. These individual spacetimes are then stitched together using asymptotic matching techniques to obtain a global solution that approximately satisfies the Einstein field equations. Precession effects are introduced by rotating the black hole spin direction according to the precessing equations of motion, in a way that is consistent with the global spacetime construction.

arXiv comment9 pages

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• Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars