1998
DOI: 10.1007/bf02575448
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Integration ofD-dimensional cosmological models with two factor spaces by reduction to the generalized Emden-Fowler equation

Abstract: The D-dimensional cosmological model on the manifold M = R × M 1 × 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 genera… Show more

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Cited by 9 publications
(10 citation statements)
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“…Hence, we find that equation (66) under the change of variables (72) passes the singularity test, and the algebraic solution is given by the Right Painlevé Series…”
Section: If We Choosementioning
confidence: 91%
See 1 more Smart Citation
“…Hence, we find that equation (66) under the change of variables (72) passes the singularity test, and the algebraic solution is given by the Right Painlevé Series…”
Section: If We Choosementioning
confidence: 91%
“…is the potential function of the system. [66]. This is not the case for the fully anisotropic Bianchi type IX in vacuum and as well for the more general system described by (33).…”
Section: B the Mini-superspace Lagrangianmentioning
confidence: 92%
“…Among the solutions [106] there exists a special class of Milne-type solutions. Recently some interesting extensions of 2-component solutions were obtained in [107].…”
Section: Multidimensional Modelsmentioning
confidence: 99%
“…where we assume b (1) and b (2) to be both nonzero, linearly independent vectors on R 2 . The conditions for such a system to be integrable are known [58,59], b = b (1) − b (2) needs to be an isotropic vector, i.e. b µ b µ = 0.…”
Section: Example 4 a Non-integrable Pseudo-euclidean Toda Systemmentioning
confidence: 99%
“…The same is not true for the pseudo-Euclidean case where the metric of the kinetic part has a Lorentzian signature. However, there exist some known integrable cases of such systems [58]. In two dimensions a generalized pseudo-Euclidean (g µν = diag(−1, 1)) Toda system with a two part contribution in the potential can be written as (we present the parametrization invariant version of system)…”
Section: Example 4 a Non-integrable Pseudo-euclidean Toda Systemmentioning
confidence: 99%