Inspiralling, Non-Precessing, Spinning Black Hole Binary Spacetime via
  Asymptotic Matching
  We construct a new global, fully analytic, approximate spacetime which
accurately describes the dynamics of non-precessing, spinning black hole
binaries during the inspiral phase of the relativistic merger process. This
approximate solution of the vacuum Einstein's equations can be obtained by
asymptotically matching perturbed Kerr solutions near the two black holes to a
post-Newtonian metric valid far from the two black holes. This metric is then
matched to a post-Minkowskian metric even farther out in the wave zone. The
procedure of asymptotic matching is generalized to be valid on all spatial
hypersurfaces, instead of a small group of initial hypersurfaces discussed in
previous works. This metric is well suited for long term dynamical simulations
of spinning black hole binary spacetimes prior to merger, such as studies of
circumbinary gas accretion which requires hundreds of binary orbits.
