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

Quantum billiards with branes on product of Einstein spaces

We consider a gravitational model in dimension D with several forms, l scalar fields and a Lambda-term. We study cosmological-type block-diagonal metrics defined on a product of an 1-dimensional interval and n oriented Einstein spaces. As an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed the conformally covariant Wheeler-DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDW equation are found in the limit of the formation of the billiard walls. These solutions reduce the problem to the so-called quantum billiard in (n + l - 1)-dimensional hyperbolic space. Several examples of quantum billiards in the model with electric and magnetic branes, e.g. corresponding to hyperbolic Kac-Moody algebras, are considered. In the case n=2 we find a set of basis asymptotic solutions to the WDW equation and derive asymptotic solutions for the metric in the classical case.Comment: 31 pages, Latex, no figures, based on a talk at Int. Session-Conf. of the Sect. of Nucl. Phys. of PSD RAN "Physics of Fundamental Interactions", April 12-15, 2016, JINR, Dubna; few typos are eliminated, some references are updated and reordere

On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

A (n+1)-dimensional gravitational model with Gauss-Bonnet term and cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with exponential dependence of scale factors: a_i ~ exp( v^i t), i = 1, ..., n, are analysed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = \sum_{k = 1}^{n} v^k \neq 0. We prove that under certain restriction R imposed solutions with K(v) > 0 are stable while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 = v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.Comment: 20 pages, no figures, LaTex; two Remarks (1 and 4) and 7 references are adde

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

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

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 the "scattering law" for Kasner parameters appearing in asymptotics of an exact S-brane solution

A multidimensional cosmological model with scalar and form fields [1-4] is studied. An exact S-brane solution (either electric or magnetic) in a model with l scalar fields and one antisymmetric form of rank m > 1 is considered. This solution is defined on a product manifold containing n Ricci-flat factor spaces M_1, ..., M_n. In the case when the kinetic term for scalar fields is positive definite we singled out a special solution governed by the function cosh. It is shown that this special solution has Kasner-like asymptotics in the limits \tau \to + 0 and \tau \to + \infty, where \tau is a synchronous time variable. A relation between two sets of Kasner parameters \alpha_{\infty} and \alpha_0 is found. This relation, named as ``scattering law'' (SL) formula, is coinciding with the ``collision law'' (CL) formula obtained previously in [5] in a context of a billiard description of S-brane solutions near the singularity. A geometric sense of SL formula is clarified: it is shown that SL transformation is a map of a ``shadow'' part of the Kasner sphere S^{N-2} (N = n+l) onto ``illuminated'' part. This map is just a (generalized) inversion with respect to a point v located outside the Kasner sphere S^{N-2}. The shadow and illuminated parts of the Kasner sphere are defined with respect to a point-like source of light located at v. Explicit formulae for SL transformations corresponding to SM2- and SM5-brane solutions in 11-dimensional supergravity are presented.Comment: 21 pages, Latex, minor correction