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

Abstract

We extend the conformal gluing construction of Isenberg et al. [19] 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 cannot, 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.