发表机构
Stockholm University（斯德哥尔摩大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明Kasner时空在大爆炸方向上的线性稳定性，并利用拟正规模概念完整描述了其线性不稳定性，无需对称性假设。
AI 中文摘要
我们证明了Kasner时空在大爆炸方向上的线性稳定性，直至一个显式的有限维非衰减自相似解空间。增长最快的解是Taub显式Bianchi II解的线性化，描述了Kasner转变。所有其他非衰减解都是这一解的均匀类比，以及线性化的Kasner度量。关键新颖之处在于Kasner时空上拟正规模的概念，类似于稳态黑洞时空上的拟正规模。所有维度为4的静止（相对于振荡）真空大爆炸时空，从大爆炸处单个观察者的角度来看，都渐近于Kasner时空。由于Belinski、Khalatnikov和Lifschitz所 conjectured 的振荡，它们预计是高度不稳定的。本文在无对称性假设下，在线性层面提供了这种不稳定性的完整描述。
英文摘要
We prove linear stability of Kasner spacetimes in the direction of the Big Bang, up to an explicit finite dimensional space of non-decaying self-similar solutions. The fastest growing solution is the linearization of Taub's explicit Bianchi II solution, describing a Kasner transition. All other non-decaying solutions are inhomogeneous analogues of this, and the linearized Kasner metric. The key novelty is a notion of quasinormal modes on Kasner spacetimes, similar to quasinormal modes on stationary black holes spacetimes. All quiescent (as opposed to oscillatory) vacuum Big Bang spacetimes of dimension 4 are asymptotic to a Kasner spacetime from the perspective of a single observer at the Big Bang. They are expected to be highly unstable due to the oscillations conjectured by Belinski, Khalatnikov and Lifschitz. This paper provides a complete description of this instability on a linear level without symmetry assumptions.
Comments48 pages, 2 figures
