Nonlinear stability of self-gravitating massive fields. A wave-Klein–Gordon model

In recent years, significant progress has been made in understanding the global evolution of self-gravitating massive matter in the small-perturbative regime near Minkowski spacetime. To investigate the interaction between a Klein–Gordon equation and Einstein’s field equations, we developed a new ap...

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Bibliographic Details
Published in:Classical and quantum gravity 2023-08, Vol.40 (15), p.154001
Main Authors: LeFloch, Philippe G, Ma, Yue
Format: Article
Language:English
Subjects:
massive field
nonlinear stability
self-gravitating
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Summary:In recent years, significant progress has been made in understanding the global evolution of self-gravitating massive matter in the small-perturbative regime near Minkowski spacetime. To investigate the interaction between a Klein–Gordon equation and Einstein’s field equations, we developed a new approach called the Euclidean-hyperboloidal foliation method. This method involves constructing a spacetime foliation that is well-suited for deriving precise decay estimates for wave and Klein–Gordon equations in curved spacetime. In this article, we provide an overview of our method and present a complete proof for a wave-Klein–Gordon model that captures some of the key challenges associated with the Einstein-matter system.
ISSN:0264-9381
1361-6382
DOI:10.1088/1361-6382/acde31