Asymptotic gluing of shear-free hyperboloidal initial data sets
Differential Geometry
2019-12-09 v1 General Relativity and Quantum Cosmology
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.
Cite
@article{arxiv.1912.02839,
title = {Asymptotic gluing of shear-free hyperboloidal initial data sets},
author = {Paul T. Allen and James Isenberg and John M. Lee and Iva Stavrov Allen},
journal= {arXiv preprint arXiv:1912.02839},
year = {2019}
}
Comments
50 pages, 1 figure