Asymptotic gluing of shear-free hyperboloidal initial data sets

TL;DR

This paper introduces a method for asymptotically gluing shear-free hyperboloidal initial data sets in general relativity, extending previous gluing techniques to preserve shear-free conditions using specialized elliptic theory.

Contribution

It develops a new gluing procedure that maintains the shear-free condition on hyperboloidal initial data, building on and modifying earlier constructions with advanced elliptic operator theory.

Findings

Successfully preserves shear-free condition during gluing

Extends elliptic theory to weakly asymptotically hyperbolic manifolds

Provides a framework for constructing initial data in general relativity

Abstract

We present a procedure for asymptotic gluing of hyperboloidal initial data sets that preserves the shear-free condition. Our construction is modeled on a previous gluing construction by the last three named authors, but with significant modifications that incorporate the shear-free condition. We rely on the special H\"older spaces, and the corresponding theory for elliptic operators on weakly asymptotically hyperbolic manifolds, introduced by the authors and applied to the Einstein constraint equations in two previous papers.