Exotic hyperbolic gluings

TL;DR

This paper introduces a novel method for constructing non-trivial asymptotically hyperbolic initial data sets in general relativity, extending hyperbolic regions to conformal infinity through exotic gluings.

Contribution

It provides a direct construction technique for hyperbolic initial data sets using exotic gluings, advancing the understanding of asymptotically hyperbolic geometries.

Findings

Constructed non-trivial hyperbolic initial data sets

Extended hyperbolic regions to conformal infinity

Demonstrated the feasibility of exotic gluings in hyperbolic settings

Abstract

We carry out "exotic gluings" a 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.