On cosmological-type solutions in multi-dimensional model with Gauss-Bonnet term

A (n + 1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For diagonal cosmological-type metrics, the equations of motion are reduced to a set of Lagrange equations. The effective Lagrangian contains two "minisuperspace" metrics on R^n. The first one is the well-known 2-metric of pseudo-Euclidean signature and the second one is the Finslerian 4-metric that is proportional to n-dimensional Berwald-Moor 4-metric. When a "synchronous-like" time gauge is considered the equations of motion are reduced to an autonomous system of first-order differential equations. For the case of the "pure" Gauss-Bonnet model, two exact solutions with power-law and exponential dependence of scale factors (with respect to "synchronous-like" variable) are obtained. (In the cosmological case the power-law solution was considered earlier in papers of N. Deruelle, A. Toporensky, P. Tretyakov and S. Pavluchenko.) A generalization of the effective Lagrangian to the Lowelock case is conjectured. This hypothesis implies existence of exact solutions with power-law and exponential dependence of scale factors for the "pure" Lowelock model of m-th order.Comment: 24 pages, Latex, typos are eliminate

On avoiding cosmological oscillating behavior for S-brane solutions with diagonal metrics

In certain string inspired higher dimensional cosmological models it has been conjectured that there is generic, chaotic oscillating behavior near the initial singularity -- the Kasner parameters which characterize the asymptotic form of the metric "jump" between different, locally constant values and exhibit a never-ending oscillation as one approaches the singularity. In this paper we investigate a class of cosmological solutions with form fields and diagonal metrics which have a "maximal" number of composite electric S-branes. We look at two explicit examples in D=4 and D=5 dimensions that do not have chaotic oscillating behavior near the singularity. When the composite branes are replaced by non-composite branes chaotic oscillatingComment: Corrected typos, published in Phys. Rev. D72, 103511 (2005

Black-brane solution for C_2 algebra

Black p-brane solutions for a wide class of intersection rules and Ricci-flat ``internal'' spaces are considered. They are defined up to moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra C_2 is obtained. The functions H_1 and H_2 for this solution are polynomials of degree 3 and 4.Comment: 12 pages, Latex, submitted to J. Math. Phy

On analogues of black brane solutions in the model with multicomponent anisotropic fluid

A family of spherically symmetric solutions with horizon in the model with m-component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n-1 Ricci-flat "internal" spaces. The equation of state for any s-th component is defined by a vector U^s belonging to R^{n + 1}. The solutions are governed by moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M_2-M_5 configuration (in D =11 supergravity) corresponding to Lie algebra A_2 is presented.Comment: 8 pages, Latex, references and several equations and examples are added, typos are eliminate

Hyperbolic Kac-Moody Algebra from Intersecting p-branes

A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological-type solution (in 11-dimensional model with two 4-forms) related to hyperbolic Kac-Moody algebra ${\cal F}_3$ (of rank 3). This solution describes the non-Kasner power-law inflation.Comment: 15 pages, Latex. A talk presented at the Second Winter School on Branes, Fields and Math. Phys. (Seoul, Korea). Corrected version. Journ. ref.: J. Math. Phys., 40, (1999) 4072-4083; Corrigenda to appea