On the “scattering law” for Kasner parameters in the model with a one-component anisotropic fluid

Abstract

A multidimensional cosmological model with a one-component anisotropic fluid is considered. An exact solution is obtained. This solution is defined on a product manifold containing n Ricci-flat factor spaces. We single out a special solution governed by the function cosh. It is shown that this special solution has Kasner-like asymptotics in the limits τ → +0 and τ → +∞, where τ is the synchronous time variable. A relation between two sets of Kasner parameters α ∞ and α 0 is found. This formula (“scattering law”) coincides with that obtained earlier for the S-brane solution (where scalar fields are absent).