# On the billiard approach in multidimensional cosmological models

@article{Ivashchuk2008OnTB, title={On the billiard approach in multidimensional cosmological models}, author={Vladimir D. Ivashchuk and Vitaly N. Melnikov}, journal={Gravitation and Cosmology}, year={2008}, volume={15}, pages={49-58} }

A short overview of the billiard approach for cosmological-type models with n Einstein factor spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider cosmological models with a multicomponent perfect-fluid and with composite branes. The second case describes cosmological and spherically symmetric configurations in a theory with scalar fields and fields of forms. The conditions for appearance of asymptotic…

## 17 Citations

### Quantum billiards in multidimensional models with fields of forms

- Mathematics, PhysicsGravitation and Cosmology
- 2013

A Bianchi type I cosmological model in (n + 1)-dimensional gravity with several forms is considered. When the electric non-composite brane ansatz is adopted, the Wheeler-DeWitt (WDW) equation for the…

### Quantum billiards in multidimensional models with fields of forms on a product of Einstein spaces

- Mathematics
- 2016

The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an…

### Quantum billiards in multidimensional models with fields of forms on a product of Einstein spaces

- MathematicsGravitation and Cosmology
- 2016

The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an…

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

- Mathematics
- 2010

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…

### Quantum billiards with branes on product of Einstein spaces

- Mathematics
- 2016

We consider a gravitational model in dimension D with several forms, l scalar fields and a $$\Lambda $$Λ-term. We study cosmological-type block-diagonal metrics defined on a product of an…

### On Cosmological-Type Solutions in Multi-Dimensional Model with GAUSS-BONNET Term

- Mathematics, Physics
- 2010

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…

### On Brane Solutions Related to Non-Singular Kac-Moody Algebras

- Mathematics
- 2011

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 × M1 × … × Mn, where Mi are Einstein spaces (i ≥ 1).…

### Black brane solutions related to non-singular Kac-Moody algebras

- Mathematics
- 2011

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 × M1 × … × Mn, where Mi are Einstein spaces (i ≥ 1).…

### On Brane Solutions with Intersection Rules Related to Lie Algebras

- MathematicsSymmetry
- 2017

The review is devoted to exact solutions with hidden symmetries arising in a multidimensional gravitational model containing scalar fields and antisymmetric forms, and the sigma-model approach for the solutions to field equations was derived.

### Hořava–Lifshitz gravity inspired Bianchi-II cosmology and the mixmaster universe

- Physics
- 2017

We study different aspects of the Hořava-Lifshitz inspired Bianchi-II cosmology and its relations with the mixmaster universe model. First, we present exact solutions for a toy model, where only the…

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