Related papers: Kohn's theorem and Newton-Hooke symmetry for Hill'…
The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter…
$N$ "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…
We present the details of a model in general relativity of a small charged black hole moving in an external gravitational and electromagnetic field. The importance of our model lies in the fact that we can derive the equations of motion of…
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…
We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential.…
We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on…
We present here an interesting non-relativistic limit, referred to as the Newton-Hooke (NH) limit, of the purely magnetic BTZ solution by starting from the Einstein-Maxwell system in the 2+1 dimensions. The Newton-Hooke limit is different…
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…
We construct finite- and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These…
The Bargmann algebra and centrally-extended Newton-Hooke algebras describe the non-relativistic symmetries of massive particles in flat and curved spacetimes, respectively. These three algebras all arise as deformations of the universal…
We introduce a systematic and direct procedure to generate hairy rotating black holes by deforming a spherically symmetric seed solution. We develop our analysis in the context of the gravitational decoupling approach, without resorting to…
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…
We show that the attractor mechanism for generic black hole is a consequence of the double-horizon. Investigation of equations of motion shows that in the case of the double-horizon black holes, the dynamics of the geometry, the scalars and…
A covariant formulation for the Newton-Hooke particle is presented by following an algorithm developed by us \cite{BMM1, BMM2, BMM3}. It naturally leads to a coupling with the Newton-Cartan geometry. From this result we provide an…
We show how to decoupling two spherically symmetric and static gravitational sources through the most general possible extension of the so-called Minimal Geometric Deformation-decoupling. As a test, we decouple the Einstein-Maxwell system…
The paper presents equations determining the particle spin evolution in the post-Newtonian approximation in the problem of motion of two mass and spin possessing particles. The equations are derived with the Einstein-Infeld-Hoffmann method…
For composite systems made of $N$ different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first…
The decomposition of the non-commutative Landau (NCL) system into two uncoupled one-dimensional chiral components, advocated by Alvarez, Gomis, Kamimura and Plyushchay [1], is generalized to nonvanishing electric fields. This allows us to…
We prove two homotopy decomposition theorems for the loops on co-H-spaces, including a generalization of the Hilton-Milnor Theorem. These are applied to problems arising in algebra, representation theory, toric topology, and the study of…
We derive an action whose equations of motion contain the Poisson equation of Newtonian gravity. The construction requires a new notion of Newton--Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann…