Narrow Results

The paper studied classical oscillations of background metric in the multidimensional anisotropic model of Kazner in the de-Sitter stage and obtained dependence of fluctuations on dimension of spacetime with infinite expansion. Stability of the model could be achieved when the number of spacelike dimensions equals to or more than four. We calculated the contributions to the density of "vacuum energy", that are provided by proper oscillations of background metric and compared with contribution of cosmological arising from particles due to expansion. As it turned out, contribution of gravitational oscillation of metric into density of "vacuum energy" should play a significant role in the de-Sitter stage.

We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory, since the causal structure of the immersed space-time is not preserved by the immersion.