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.
Related
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BibTeX
@misc{petersen2026linear,
title = {{The linear instability of Kasner spacetimes}},
author = {Oliver Petersen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20809},
eprint = {2609.20809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20809},
}
RIS
TY - UNPB
TI - The linear instability of Kasner spacetimes
AU - Oliver Petersen
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20809
UR - https://arxiv.org/abs/2609.20809
AB - 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.
ER -