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In this work a new numerical technique to prepare Cauchy data for the initialvalue problem (IVP) formulation of Einstein's field equations is presented.Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino(2000) our (pseudo)-spectral scheme is demonstrated under the assumption ofaxisymmetry so as to fashion composite Hamiltonian constraint satisfyinginitial data featuring internal binary black holes (BBH) as glued to exteriorSchwarzschild initial data in isotropic form. The generality of the method isillustrated in a comparison of the ADM mass of EAG initial data sets featuringinternal BBHs as modelled by Brill-Lindquist and Misner data.In contrast to therecent work of Doulis and Rinne (2016), and Pook-Kolb and Giulini (2018) we donot make use of the York-Lichnerowicz conformal framework to reformulate theconstraints.

Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild