Related papers: Newton-Hooke type symmetry of anisotropic oscillat…
Hill's equations, which first arose in the study of the Earth-Moon-Sun system, admit the two-parameter centrally extended Newton-Hooke symmetry without rotations. This symmetry allows for extending Kohn's theorem about the center-of-mass…
We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as…
Motivated by the symmetry in the non-relativistic limit of anti-de Sitter geometry, we employ planar dynamical models featuring exotic (deformed) harmonic oscillators, presented through direct and indirect Lagrangian representations. The…
It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton-Hooke symmetry provided frequencies of oscillation form the arithmetic sequence omega_k=(2k-1) omega_1, where k=1,...,n, and l is the…
Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke model under the Newton-Hooke contraction of the $BdS$ spacetime with respect to the transformation group, algebra and geometry. It is shown that in Newton-Hooke…
In this thesis some systems with exotic symmetries, which are a peculiarity in 2+1 space-time dimensions, are studied. Coded in the exotic structure, there appear noncommutative coordinates and a phases structure. This kind of systems has…
It is demonstrated that, in the framework of the orbit method, a simple and damped harmonic oscillators are indistinguishable at the level of an abstract Lie algebra. This opens a possibility for treating the dissipative systems within the…
Our previous study of a system of bodies assumed to move along almost circular orbits around a central mass, approximately described by Hill's equations, is extended to "exotic" [alias non-commutative] particles. For a certain critical…
Using simple algebraic methods along with an analogy to the BFSS model, we explore the possible (target) spacetime symmetries that may appear in a matrix description of de Sitter gravity. Such symmetry groups could arise in two ways, one…
An exact spherically symmetric black hole solution of a recently proposed noncommutative gravity theory based on star products and twists is constructed. This is the first nontrivial exact solution of that theory. The resulting…
Anisotropic spherically symmetric solutions within the framework of the Brans-Dicke theory are uncovered through a unique gravitational decoupling approach involving a minimal geometric transformation. This transformation effectively…
A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction…
We find a new family of galactic metrics corresponding to flat rotation curves at the outer radii. These are vacuum solutions to a gravity theory where the Newton's coupling varies mildly in space. The effective `mass', whose origin is…
In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric…
$N$ "exotic" [alias non-commutative] particles with masses $m_a$, charges $e_a$ and non-commutative parameters $\theta_a$, moving in a uniform magnetic field $B$, separate into center-of-mass and internal motions if Kohn's condition…
Newton-Hooke group is the nonrelativistic limit of de Sitter (anti-de Sitter) group, which can be enlarged with transformations that describe constant acceleration, as well as central charges. We consider a higher order Lagrangian that is…
A nonsymmetric gravitational theory (NGT) is presented which is free of ghost poles, tachyons and higher-order poles and there are no problems with asymptotic boundary conditions. An extended Birkhoff theorem is shown to hold for the…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
We show how the Newton-Hooke (NH) symmetries, representing a nonrelativistic version of de-Sitter symmetries, can be enlarged by a pair of translation vectors describing in Galilean limit the class of accelerations linear in time. We study…
A class of exact solutions of Einstein's equations is analysed which describes uniformly accelerating charged black holes in an asymptotically de Sitter universe. This is a generalisation of the C-metric which includes a cosmological…