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Main Authors: Avalos, Rodrigo, Lira, Jorge, Marque, Nicolas
Format: Preprint
Published: 2022
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Online Access:https://arxiv.org/abs/2201.08347
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author Avalos, Rodrigo
Lira, Jorge
Marque, Nicolas
author_facet Avalos, Rodrigo
Lira, Jorge
Marque, Nicolas
contents In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological space-times with non-compact Cauchy hypersurfaces, which favour general bounded geometry manifolds rather than a specific model for infinity. First, we prove an existence criterion on complete manifolds with appropriate barrier functions for physically well-motivated coupled systems. Then, in the bounded geometry case, we build barrier functions and thus show existence. We also prove an existence result on compact manifolds with boundary for a wider family of coupled systems.
format Preprint
id arxiv_https___arxiv_org_abs_2201_08347
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Einstein Type Systems on Complete Manifolds
Avalos, Rodrigo
Lira, Jorge
Marque, Nicolas
Analysis of PDEs
Mathematical Physics
35J60, 58J05, 83C05
In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological space-times with non-compact Cauchy hypersurfaces, which favour general bounded geometry manifolds rather than a specific model for infinity. First, we prove an existence criterion on complete manifolds with appropriate barrier functions for physically well-motivated coupled systems. Then, in the bounded geometry case, we build barrier functions and thus show existence. We also prove an existence result on compact manifolds with boundary for a wider family of coupled systems.
title Einstein Type Systems on Complete Manifolds
topic Analysis of PDEs
Mathematical Physics
35J60, 58J05, 83C05
url https://arxiv.org/abs/2201.08347