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We present a detailed description of techniques developed to combine 3Dnumerical simulations and, subsequently, a single black hole close-limitapproximation. This method has made it possible to compute the first completewaveforms covering the post-orbital dynamics of a binary black hole system withthe numerical simulation covering the essential non-linear interaction beforethe close limit becomes applicable for the late time dynamics. To determinewhen close-limit perturbation theory is applicable we apply a combination ofinvariant a priori estimates and a posteriori consistency checks of therobustness of our results against exchange of linear and non-linear treatmentsnear the interface. Once the numerically modeled binary system reaches a regimethat can be treated as perturbations of the Kerr spacetime, we mustapproximately relate the numerical coordinates to the perturbative backgroundcoordinates. We also perform a rotation of a numerically defined tetrad toasymptotically reproduce the tetrad required in the perturbative treatment. Wecan then produce numerical Cauchy data for the close-limit evolution in theform of the Weyl scalar $\psi_4$ and its time derivative $\partial_t\psi_4$with both objects being first order coordinate and tetrad invariant. TheTeukolsky equation in Boyer-Lindquist coordinates is adopted to furthercontinue the evolution. To illustrate the application of these techniques weevolve a single Kerr hole and compute the spurious radiation as a measure ofthe error of the whole procedure. We also briefly discuss the extension of theproject to make use of improved full numerical evolutions and outline theapproach to a full understanding of astrophysical black hole binary systemswhich we can now pursue.Comment: New typos found in the version appeared in PRD. (Mostly found and  collected by Bernard Kelly

The Lazarus project: A pragmatic approach to binary black hole evolutions