2025/06/26 by Cécile Huneau, Huneau, Cécile, Jonathan Luk +1
Mathematics · #Gas Dynamics and Kinetic Theory #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems
paper · pdf · doi:10.48550/arxiv.2506.21779
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.