A gluing construction for non-vacuum solutions of the Einstein constraint equations

TL;DR

This paper generalizes the conformal gluing method for Einstein's equations to include matter fields like fluids and gauge fields, extending its applicability to higher dimensions and various non-vacuum theories.

Contribution

It introduces an extended conformal gluing construction for Einstein's equations coupled with matter fields, clarifying criteria for its application across different non-vacuum theories.

Findings

Extended gluing technique to matter-coupled Einstein equations.

Applicable to higher dimensions and various matter fields.

Clarified criteria for applying the construction to different theories.

Abstract

We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical fields such as perfect fluids and the Yang-Mills equations as well as the Einstein-Vlasov system, which is an important example coming from kinetic theory. In carrying out these extensions, we extend the conformal gluing technique to higher dimensions and codify it in such a way as to make more transparent where it can, and can not, be applied. In particular, we show exactly what criteria need to be met in order to apply the construction, in its present form, to any other non-vacuum field theory.