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Qualitative analysis of ten-dimensional lovelock cosmological models ; De Rop, Yves ; et al in General Relativity & Gravitation (1992), 24 The Einstein-like field equations obtained from the variation of a Lagrangian containing linear, quadratic (Gauss-Bonnet) and quartic terms for a ten-dimensional cosmological model cannot be solved ... [more ▼] The Einstein-like field equations obtained from the variation of a Lagrangian containing linear, quadratic (Gauss-Bonnet) and quartic terms for a ten-dimensional cosmological model cannot be solved analytically. However, we can reduce them to a system of dynamical equations for the “Hubble parameters”. The study of the mathematical properties of the fixed points of this system gives a qualitative picture of the behaviour of a class of possible solutions. The inclusion of a quartic term generates an extremely rich structure for the corresponding dynamical system. Some solutions are shown to exhibit the interesting property of dimensional reduction, which has been proposed as a possible explanation of the three-dimensional character of our universe. [less ▲] Detailed reference viewed: 12 (1 ULg)Qualitative approach of the general vacuum Bianchi VI and VII cosmological models near the singularity De Rop, Yves in General Relativity & Gravitation (1989), 21 We first show that the chaos-generating terms are absent from the vacuum field equations in the case of the general Bianchi VI and VII cosmological models. According to recent studies, this proves that ... [more ▼] We first show that the chaos-generating terms are absent from the vacuum field equations in the case of the general Bianchi VI and VII cosmological models. According to recent studies, this proves that the Kasnerian metric is a general solution for these models in the neighborhood of the initial singularity. Then, using a method developed by Jantzen, we reduce the field equations to a nonautonomous system of order two. A numerical integration leads to the explicit four-parameter asymptotic form of a general solution, which is indeed Kasnerian in the canonical invariant basis. [less ▲] Detailed reference viewed: 14 (2 ULg)Using EXCALC to study nondiagonal multidimensional spatially homogeneous cosmologies. De Rop, Yves ; in General Relativity & Gravitation (1988), 20 The exterior calculus package EXCALC2, developed by Schrüfer, is used to implement Siklos' method on a computer. By an appropriate choice of the 1-form basis of spatially homogeneous cosmological models ... [more ▼] The exterior calculus package EXCALC2, developed by Schrüfer, is used to implement Siklos' method on a computer. By an appropriate choice of the 1-form basis of spatially homogeneous cosmological models, making use of the time-dependent automorphisms of the Lie algebra, it is possible to obtain a compact form of Einstein's field equations for general models of this type. The explicit expression of the equations, obtained with the help of EXCALC2, is given here for two nondiagonal five-dimensional spatially homogeneous models, namely G[SUB]1[/SUB] and G[SUB]8[/SUB]. These equations constitute an ideal tool for the study of the dynamics of these models: an oscillatory behavior has been found for model G[SUB]1[/SUB], while model G[SUB]8[/SUB] exhibits a monotonous kasnerian mode of approach to the initial singularity. [less ▲] Detailed reference viewed: 13 (0 ULg) |
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