Using EXCALC to study nondiagonal multidimensional spatially homogeneous cosmologies

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 G₁ and G₈. These equations constitute an ideal tool for the study of the dynamics of these models: an oscillatory behavior has been found for model G₁, while model G₈ exhibits a monotonous kasnerian mode of approach to the initial singularity.