Nonlinear stability of self-gravitating massive fields. A wave-Klein-Gordon model. (English) Zbl 1517.83063
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.
MSC:
| 83E05 | Geometrodynamics and the holographic principle |
| 35B20 | Perturbations in context of PDEs |
| 51B20 | Minkowski geometries in nonlinear incidence geometry |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 81U90 | Particle decays |
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