Related papers: Billiard Representation for Multidimensional Cosmo…
This work presents some results regarding three-dimensional billiards having a non-constant potential of Keplerian type inside a regular domain $D\subset \mathcal R^3$. Two models will be analysed: in the first one, only an inner Keplerian…
N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal…
A class of non-compact billiards is introduced, namely the infinite step billiards, i.e., systems of a point particle moving freely in the domain $\Omega = \bigcup_{n\in\N} [n,n+1] \times [0,p_n]$, with elastic reflections on the boundary;…
We study the classical and quantum cosmology of a universe in which the matter content is a perfect fluid and the background geometry is described by a Bianchi type I metric. To write the Hamiltonian of the perfect fluid we use the Schutz…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between…
The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states…
We consider the billiard in the exterior of a piecewise smooth body in two-dimensional Euclidean space and show that the maximum number of directions of invisibility in such billiard is at most finite.
We investigate $(n+1)$-dimensional string-dilaton cosmology with effective dilaton potential in presence of perfect-fluid matter.We get exact solutions parametrized by the constant $\gam$ of the state equation $p=(\gam-1)\rho$, the spatial…
We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The…
We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is…
We show that combinations of (in general, non-linear) 2- and 3-form fields analogous to the Maxwell (1-form) field, completely describe perfect fluids, including the rotating ones. In the non-rotating case, the 2-form field in sufficient,…
A body moves in a medium composed of noninteracting point particles; interaction of particles with the body is absolutely elastic. It is required to find the body's shape minimizing or maximizing resistance of the medium to its motion. This…
In this work, we study cosmological solutions of the 8-dimensional Einstein Yang-Mills theory coupled to a perfect-fluid matter. A Yang-Mills instanton of extra dimensions causes a 4-dimensional expanding universe with dynamical…
A physicaly reasonable interpretation is provided for the perfect fluid, sphericaly symmetric, conformally flat ``Stephani Universes''. The free parameters of this class of exact solutions are determined so that the ideal gas relation $p=n…
In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled…
In the present paper we derive the Wigner current of the particle in a multidimensional billiard -- the compact region of space in which the particle moves freely. The calculation is based on proposed by us previously method of imposing…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
We study the asymptotic dynamics of the Mixmaster Universe, near the cosmological singularity, considering $f(R)$ gravity up to a quadratic corrections in the Ricci scalar $R$. The analysis is performed in the scalar-tensor framework and…
We consider the static and spherically symmetric field equations of general relativity for charged perfect fluid spheres in the presence of a cosmological constant. Following work by Florides (1983) we find new exact solutions of the field…
Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ to the…