We carry out “exotic gluings” à la Carlotto–Schoen for asymptotically hyperbolic general relativistic initial data sets. In particular, we obtain a direct construction of non-trivial initial data sets which are exactly hyperbolic in large regions extending to conformal infinity.
"Exotic hyperbolic gluings." J. Differential Geom. 108 (2) 243 - 293, February 2018. https://doi.org/10.4310/jdg/1518490818