The Conformal Einstein Field Equations with Massless Vlasov Matter

Joudioux, Jérémie; Thaller , Maximilian; Kroon , Juan A. Valiente

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The Conformal Einstein Field Equations with Massless Vlasov Matter

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Joudioux, Jérémie
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1903.12251.pdf
(プレプリント), 388KB

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引用

Joudioux, J., Thaller, M., & Kroon, J. A. V. (in press). The Conformal Einstein Field Equations with Massless Vlasov Matter. Annales de l'Institut Fourier. Retrieved from http://arxiv.org/abs/1903.12251.

引用: https://hdl.handle.net/21.11116/0000-0003-484F-5

要旨

We prove the stability of de Sitter space-time as a solution to the
Einstein-Vlasov system with massless particles. The semi-global stability of
Minkowski space-time is also addressed. The proof relies on conformal
techniques, namely Friedrich's conformal Einstein field equations. We exploit
the conformal invariance of the massless Vlasov equation on the cotangent
bundle and adapt Kato's local existence theorem for symmetric hyperbolic
systems to prove a long enough time of existence for solutions of the evolution
system implied by the Vlasov equation and the conformal Einstein field
equations.