Related papers: Closed, spirograph-like orbits in power law centra…
We present exact black hole solutions endowed with magnetic charge coming from exponential and logarithmic nonlinear electrodynamics (NLED). Classically, we analyze the null and timelike geodesics, all of which contain both the bound and…
Let $R$ be a finite ring and define the hyperbola $H=\{(x,y) \in R \times R: xy=1 \}$. Suppose that for a sequence of finite odd order rings of size tending to infinity, the following "square root law" bound holds with a constant $C>0$ for…
We calculate the precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
We consider a charged quantum particle immersed in an axial magnetic field, comprising a local Aharonov-Bohm singularity and a regular perturbation. Quadratic form techniques are used to characterize different self-adjoint realizations of…
We present the gravitational-wave flux balance law in an extreme mass-ratio binary with a spinning secondary. This law relates the flux of energy (angular momentum) radiated to null infinity and through the event horizon to the local change…
The Witt ring of symmetric bilinear forms over a field has divided power operations. On the other hand, it follows from Garibaldi-Merkurjev-Serre's work on cohomological invariants that all operations on the Witt ring are essentially linear…
A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. They are the pseudoclassical basis of the positive energy $({1\over 2},0)$ [or…
Using the wrapped Floer homology, we prove the existence of consecutive collisions at the primaries in the circular restricted three-body problem. We also prove the existence of a symmetric periodic orbit. These existence results are…
The Aharonov-Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to…
In this paper, we study pseudo-rotations of the open annulus, \emph{i.e.} conservative homeomorphisms of the open annulus whose rotation set is reduced to a single irrational number (the angle of the pseudo-rotation). We prove in particular…
We derive the radial action of a spinning probe particle in Kerr spacetime from the worldline formalism in the first-order form, focusing on linear in spin effects. We then develop a novel covariant Dirac bracket formalism to compute the…
We consider magnetospheric structure of rotating neutron stars with internally twisted axisymmetric magnetic fields. The twist-induced and rotation-induced toroidal magnetic fields align/counter-align in different hemispheres. Using…
We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…
Properties of the optical reference geometry related to Kerr-Newman black-hole and naked-singularity spacetimes are illustrated using embedding diagrams of their equatorial plane. Among all inertial forces defined in the framework of the…
Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known $1/r$ (Keplerian) and logarithmic…
We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering set consisting of the finite number of critical elements (i.e., singularities or closed orbits).…
The properties of modified Hayward black hole space-time can be investigated through analyzing the particle geodesics. By means of a detailed analysis of the corresponding effective potentials for a massive particle, we find all possible…