The Bianchi Ix (MIXMASTER) Cosmological Model is Not Integrable
A.~Latifi (Universit\'e libre de Bruxelles), M.~Musette (Vrije, Universiteit Brussel), R.~Conte (CEA, Centre d'\'etudes de Saclay)
TL;DR
This paper proves that the Bianchi IX (MIXMASTER) cosmological model cannot be integrated analytically by demonstrating the presence of a movable transcendental essential singularity and applying the Painlevé test.
Contribution
It establishes the nonintegrability of the Bianchi IX model and confirms the uniqueness of known vacuum solutions through perturbative analysis.
Findings
The model exhibits a movable transcendental essential singularity.
No additional closed-form vacuum solutions exist beyond the known three.
The perturbative Painlevé test confirms nonintegrability.
Abstract
The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the perturbative Painlev\'e test; this proves the inexistence of any vacuum solution other than the three known ones.
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Taxonomy
TopicsSolar and Space Plasma Dynamics · Cosmology and Gravitation Theories · Geophysics and Gravity Measurements