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The effective potential energy of the particles in the field of rotating uniformly magnetized celestial body is investigated. The axis of rotation coincides with the axis of the magnetic field. Electromagnetic field of the body is composed…
We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…
In two dimensions a microscopic theory providing a basis for the naive analogy between a quantized vortex in a superfluid and an electron in a uniform magnetic field is presented. Following the variational approach developed by Peierls,…
The theory considered interprets gravity as a pressure force. Thus, the scalar gravitational field defines the gravity acceleration field. However, it also determines the relation between the flat ``background metric'' and a curved…
The electromagnetic force on a polarizable particle is calculated in a covariant framework. Local equilibrium temperatures for the electromagnetic field and the particle's dipole moment are assumed, using a relativistic formulation of the…
Near a black hole or an ultracompact star, motion of particles is governed by strong gravitational field. Electrically charged particles feel also electromagnetic force arising due to currents inside the star or plasma circling around. We…
A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the…
While most fundamental interactions in nature are known to be mediated by quantized fields, the possibility has been raised that gravity may behave differently. Making this concept precise enough to test requires consistent models. Here we…
In this paper, the equations of motion for geodesics in the neutral rotating Black Ring metric are derived and the separability of these equations is considered. The bulk of the paper is concerned with sets of solutions where the geodesic…
In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein's celebrated energy-mass relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian mechanics…
A famous result by Delort about the two-dimensional incompressible Euler equations is the existence of weak solutions when the initial vorticity is a diffuse bounded Radon measure with distinguished sign. In this paper we are interested in…
While the orbital eccentricity is a key feature of the gravitational two-body problem, providing an unambiguous definition in general relativity poses significant challenges. Despite such foundational issue, the eccentricity of binary black…
We study the restricted motion of an electric charge in a spherical surface in the field of a magnetic dipole. This is the classical non-relativistic St\"oermer problem within a sphere, with the dipole in its centre. We start from a…
We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing…
A relativistic electron uniformly rotating along an equatorial orbit around a dielectric ball may generate Cherenkov radiation tens of times more intense as that in case of revolution of a particle in a continuous, infinite and transparent…
Static 2-2-hole solutions of quadratic gravity have been investigated to be a possible horizonless replacement for black holes as the endpoint of gravitational collapse. Realistically such objects will form with spin, but rotating 2-2-hole…
The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
Using the method of retarded potentials approximate formulas are obtained that describe the electromagnetic field outside the relativistic uniform system in the form of a charged sphere rotating at a constant speed. For the near, middle and…
The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.