Asymptotic Gluing of Shear-Free Hyperboloidal Initial Data Sets

We present a procedure for asymptotic gluing of hyperboloidal initial data sets the Einstein field equations that preserves shear-free condition. Our construction is modeled on in Isenberg et al. (Ann Henri Poincare 11(5):881–927, 2010), but with significant modifications incorporate rely special Holder spaces, and corresponding theory elliptic operators weakly asymptotically hyperbolic manifolds, introduced by authors Allen (Commun Anal Geom 26(1):1–61, 2018) applied to constraint (Class Quantum Grav 33(11):115015, 2016).