Related papers: Three-Dimensional Billiards with Time Machine
In this paper, we define a variant of billiards in which the ball bounces around a square grid erasing walls as it goes. We prove that there exist periodic tunnels with arbitrarily large period from any possible starting point, that there…
We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the…
We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…
We propose a toy model for study merger transitions in a curved spaceime with an arbitrary number of dimensions. This model includes a bulk N-dimensional static spherically symmetric black hole and a test D-dimensional brane interacting…
A right triangular billiard system is equivalent to the system of two colliding particles confined in a one-dimensional box. In spite of their seeming simplicity, no definite conclusion has been drawn so far concerning their ergodic…
Quantum dynamica of a massless Dirac particle in time-dependent 1D box and circular billiard with time-dependent radius is studied. An exact analytical wave functions and eigenvalues are obtained for the case of linear time-dependence of…
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 dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual…
Some problems of the space-time causal structure are discussed using models with traversable wormholes. For this purpose the conditions of traversable wormhole matching with the exterior space-time are considered in detail and a mixed…
Closed time-like curves naturally appear in a variety of chronology-violating space-times. In these space-times, the Principle of Self-Consistency demands an harmony between local and global affairs that excludes grandfather-like paradoxes.…
The causality properties of space-time models with traversable wormholes are considered. It is shown that relativity principle cannot be applied to the motion of the wormhole's mouths in the outer space and the dynamical wormhole…
We study the dynamical properties of a particle in a non-planar square billiard. The plane of the billiard has a sinusoidal shape. We consider both the static and time-dependent plane. We study the affect of different parameters that…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
We study the convergence towards the equilibrium for a dissipative and stochastic time-dependent oval billiard. The dynamics of the system is described by using a generic four dimensional nonlinear map for the variables: the angular…
It is well-known that a particle falling into a black hole will definitely reach the center in finite proper time if it enters the sphere of radius $3r_{s}/2$ where $r_{s}$ is the Schwarzschild radius. It is usually assumed that once the…
A brane world model is investigated, in which there are many branes that may intersect and self intersect. One of the branes, being a 3-brane, represents our spacetime, while the other branes, if they intersect our brane world, manifest…
We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…
We study collisions of massive pointlike particles in three dimensional anti-de Sitter space, generalizing the work on massless particles in [1]. We show how to construct exact solutions corresponding to the formation of either a black hole…
2+1 dimensional anti-de Sitter space has been the subject of much recent investigation. Studies of the behaviour of point particles in this space have given us a greater understanding of the BTZ black hole solutions produced by topological…
We study nonlinear dynamics of the kicked particle whose motion is confined by square billiard. The kick source is considered as localized at the center of square with central symmetric spatial distribution. It is found that ensemble…