2022/01/20 by Avalos, Rodrigo, Lira, Jorge, Marque, Nicolas
#35J60 #58J05 #83C05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2201.08347
In the present paper, we study the coupled Einstein Constraint Equations (ECE) on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. In particular, we do not impose any specific model for infinity being motivated to account for initial data sets of bounded geometry, which we take to be physically well motivated by standard cosmological space-times with non-compact Cauchy hypersurfaces. First, we prove an existence criteria on compact manifolds with boundary which applies to more general systems and can be seen as a natural extension of known existence theory for the coupled ECE. Building on this, we prove an existence criterium on complete manifolds with appropriate barrier functions for a family of physically well-motivated coupled systems on complete manifolds. Finally, we build barrier functions and thus show existence in the bounded geometry case.