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arXiv · 2201.08347

Einstein Type Systems on Complete Manifolds

Rodrigo Avalos·Jorge Lira·Nicolas Marque
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Abstract

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.

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Rodrigo Avalos, Jorge Lira, Nicolas Marque. 2022-01-20. Einstein Type Systems on Complete Manifolds. https://arxiv.org/abs/2201.08347

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