2023/08/29 by Robert Conte, Conte, Robert · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #33E17 #34Mxx #35Q99 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements
paper · doi:10.48550/arxiv.2308.15604
openalex publication_date 2023/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the six-dimensional dynamical system in three components introduced by Ryan to describe the scenario of Belinskii, Khalatnikov and Lifshitz to the cosmological singularity when the spatial metric tensor is not diagonal. Despite its nonintegrability, recently proven by Goldstein and Piechocki, the three four-dimensional systems defined by canceling one of the three components happen to be integrable. We express their general solution as a rational function of, respectively, two exponential functions, a third Painlevé function, two exponential functions.