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arXiv · 2603.13104

The Bianchi IX Attractor in Modified Gravity

Ester Beatriz·Everaldo Bonotto·Phillipo Lappicy
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Abstract

We consider vacuum anisotropic spatially homogeneous models in certain modified gravity theories (such as Ho\v{r}ava-Lifshitz, $\lambda$-$R$ or $f(R)$ gravity), which are expected to describe generic spacelike singularities for these theories. These models perturb the well-known Bianchi models in general relativity (GR) by a parameter $v\in (0,1)$ with GR recovered at $v=1/2$. We prove an analogue of the well-known Ringstr\"om attractor theorem in GR to the supercritical theories: for any $v\in (1/2,1)$, all solutions of Bianchi type $\mathrm{IX}$ converge to an analogue of the Mixmaster attractor, consisting of Bianchi type I solutions (Kasner states) and heteroclinic chains of Bianchi type II solutions. In contrast to GR, there are no solutions that converge to a different set other than the Mixmaster (such as the locally rotationally symmetric solutions in GR).

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Ester Beatriz, Everaldo Bonotto, Phillipo Lappicy. 2026-03-13. The Bianchi IX Attractor in Modified Gravity. https://arxiv.org/abs/2603.13104

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