In order to construct asymptotically Euclidean, Einstein's initial data sets, we introduce the localized seed-to-solution method and establish the existence of classes of data sets that exhibit the gravity shielding phenomenon (or localization). We achieve optimal shielding in the sense that the gluing domain can be a collection of arbitrarily narrow nested cones while the metric and extrinsic curvature may be controlled at a super-harmonic rate, and may have arbitrarily slow decay (possibly beyond the standard ADM formalism). We also uncover several notions of physical and mathematical interest: normalized asymptotic kernel elements, localized energy functionals, localized ADM modulators, and relative energy-momentum vectors.
Comment: 9 pages