# Gluing for the constraints for higher spin fields

## TL;DR

This paper extends a method for manipulating initial data constraints from Maxwell and linearized gravity to higher spin fields, using a generalized de Rham complex and elliptic theory.

## Contribution

It introduces a generalized gluing and shielding procedure for higher spin fields based on a higher spin de Rham complex and elliptic analysis.

## Key findings

- Established a potential-based parametrization of constraints for higher spin fields.
- Proved the existence of potentials for solutions to higher spin field constraints.
- Generalized the gluing technique to a broader class of fields.

## Abstract

This short note is a follow-up on the paper by Beig and Chru\'sciel regarding the use of potentials to perform a gluing and shielding of initial data for Maxwell fields and linearised gravity. Based on a work in collaboration with Andersson and B\"ackdahl, 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 for solutions to the constraints for higher spin fields.