Nonlinear stability of self-gravitating massive fields. A wave-Klein-Gordon model
arXiv:2212.07463 · doi:10.1088/1361-6382/acde31
Abstract
Significant advances were made in recent years on the global evolution problem for self-gravitating massive matter in the small-perturbative regime close to Minkowski spacetime. To study the coupling between a Klein-Gordon equation and Einstein's field equations, we introduced the ``Euclidean-hyperboloidal foliation method'', which is based on the construction of a spacetime foliation adapted to the derivation of sharp decay estimates for wave and Klein-Gordon equations in a curved spacetime. We give here an outline of this method, together with a full proof for a wave-Klein-Gordon model which retains some main challenges arising with the Einstein-matter system.
arXiv comment36 pages. arXiv admin note: text overlap with arXiv:1712.10045
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