Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation

Abstract

The D-dimensional cosmological model on the manifold $M=R\times M_1\times M_2$ describing the evolution of 2 Einsteinian factor spaces, $M_1$ and $M_2$, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of the perfect fluid components are both equal to 2, the Einstein equations for the model are reduced to the generalized Emden-Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin within discrete-group analysis. Using the integrable classes of this equation one generates the integrable cosmological models. The corresponding metrics are presented. The method is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$ and the 2-component perfect fluid source.

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References in corpus (2)

• Spacetime as a membrane in higher dimensions
• Exact Solutions in Multidimensional Cosmology with Shear and Bulk Viscosity

Cited by in corpus (3)

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• Bianchi IX cosmologies in the Einstein-Skyrme system in a sector with non-trivial topological charge
• Quadratic first integrals of constrained autonomous conservative dynamical systems with fixed energy