Manifold structures for sets of solutions of the general relativistic constraint equations

TL;DR

This paper develops manifold structures on different sets of solutions to the general relativistic initial data constraints, providing a mathematical framework for analyzing these solution spaces.

Contribution

It introduces a novel approach to constructing manifold structures on solution sets of the Einstein constraint equations.

Findings

Established manifold structures for solution sets

Provided a rigorous mathematical framework

Facilitated analysis of solution spaces in general relativity

Abstract

We construct manifold structures on various sets of solutions of the general relativistic initial data sets.