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.
@article{arxiv.1608.01033,
title = {Spinning, Precessing, Black Hole Binary Spacetime via Asymptotic Matching},
author = {Hiroyuki Nakano and Brennan Ireland and Manuela Campanelli and Eric J. West},
journal= {arXiv preprint arXiv:1608.01033},
year = {2016}
}