{"ID":23551629,"CreatedAt":"2026-09-18T04:14:56.806955139Z","UpdatedAt":"2026-09-18T04:14:56.806955139Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20809","arxiv_id":"2609.20809","title":"The linear instability of Kasner spacetimes","abstract":"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.","short_abstract":"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 a...","url_abs":"https://arxiv.org/abs/2609.20809","url_pdf":"https://arxiv.org/pdf/2609.20809v1","authors":"[\"Oliver Petersen\"]","published":"2026-09-17T17:58:33Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"gr-qc\",\"math.DG\"]","methods":"[]","has_code":false}