Gluing for the constraints for higher spin fields

Abstract

This note is a follow-up on the paper by Beig and Chruściel regarding the use of potentials to perform gluing and shielding of initial data for Maxwell fields and linearised gravity. Based on a work in collaboration with Andersson and Bäckdahl, this gluing and shielding procedure is generalised to higher spin fields. The approach is based on a generalisation of the de Rham complex to higher spin fields providing a parametrization of the set of constraints, as well as standard elliptic theory to prove the existence of a potential.