We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact characterization of high-frequency limits of vacuum spacetimes as solutions to the Einstein–massless Vlasov system. Some open problems and future directions are discussed.

中文翻译：

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爱因斯坦方程的高频解


我们回顾了有关爱因斯坦真空方程高频解以及这些解的极限的最新数学结果。我们特别关注伯内特的两个猜想，它们试图给出真空时空高频极限的精确表征，作为爱因斯坦无质量弗拉索夫系统的解。讨论了一些悬而未决的问题和未来的方向。