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In this work, we introduce a spectral-infinite element method for solvingEinstein's constraint equations in hyperbolic form. As an application of this,we use this method for computing asymptotically flat perturbations of a Kerrblack hole with small angular momentum. Our numerical infrastructure is basedon the use of a spin-weighted spherical harmonic transform combined with aninfinite element method for solving partial differential equations in unboundeddomains.

Spectral-infinite element method approach for computing asymptotically flat initial data sets in general relativity