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arXiv · 2506.21779

High-frequency backreaction for the Einstein equations under $\mathbb U(1)$ symmetry: from Einstein-dust to Einstein-Vlasov

Cécile Huneau·Jonathan Luk
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Abstract

Given suitable small, localized, $\mathbb U(1)$-symmetric solutions to the Einstein-massless Vlasov system in an elliptic gauge, we prove that they can be approximated by high-frequency vacuum spacetimes. This extends previous constructions where the limiting spacetime solves the Einstein-(multiple) null dust system (i.e., where the limiting massless Vlasov field can be written as a finite sum of delta measures). The proof proceeds by first approximating solutions to the Einstein-massless Vlasov system by solutions to the Einstein-(multiple) null dust system, then approximating solutions to the Einstein-null dust system by vacuum solutions. In the process, we take the number of families of dusts to infinity.

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Cécile Huneau, Jonathan Luk. 2025-06-26. High-frequency backreaction for the Einstein equations under $\mathbb U(1)$ symmetry: from Einstein-dust to Einstein-Vlasov. https://arxiv.org/abs/2506.21779

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