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Electrons obeying the Dirac equation are investigated under the non-relativistic $c \mapsto \infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the…
A new class of 3D anisotropic analytic solutions of relativistic hydrodynamics with constant pressure is found. We analyse, in particular, solutions corresponding to ellipsoidally symmetric expansion of finite systems into vacuum. They can…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
The field of an electromagnetic (E) dipole has been examined using general relativistic (R) and quantum mechanical (Q) points of view, and an E=Q=R equivalence principle presented whereas the curvature of the electromagnetic streamlines of…
The solutions of the London equations for the magnetic field expulsion from superconductors are presented in this paper for the cylindrical symmetry. The result is analyzed in detail and represented numerically for the case of a uniform…
In order to shed some light in the meaning of the relativistic multipolar expansions we consider different static solutions of the axially symmetric vacuum Einstein equations that in the non relativistic limit have same Newtonian moments.…
The Lorentz force equations provide a partial description of the geodesic motion of a charged particle on a four-manifold. Under the hypothesis that Maxwell's equations express symmetry properties of the Ricci tensor, the full…
This paper presents an intuitive, geometrical derivation of the relativistic addition of velocities, and of the electromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional…
There are no known analytic solutions to the force-free magnetic field equations in coordinates representing Dupin cyclides. The fact that the curvature lines of Dupin cyclides are all circles is used here to derive a force-free magnetic…
The electric permittivities and magnetic permeabilities for a relativistic electron gas are calculated from quantum electrodynamics at finite temperature and density as functions of temperature, chemical potential, frequency, and…
The local and global properties of the Levi-Civita (LC) solutions coupled with an electromagnetic field are studied and some limits to the vacuum LC solutions are given. By doing such limits, the physical and geometrical interpretations of…
Dynamics of relativistic outflows along the rotation axis of a Kerr black hole is investigated using a simple model that takes into account the relativistic tidal force of the central source as well as the Lorentz force due to the…
The magnetic flux distribution is determined by the solution of the Grad-Shafranov equation. With differential rotation, i.e. the variation of the iso-rotation parameter, the shape of the light surface must be calculated in an iterative…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the…
The paper explores a plane symmetric cosmological model within the framework of the Lyra manifold, incorporating interactions among various fields. These fields include a charged perfect fluid, a mass-less scalar field, and an…
We discuss how to obtain the nonrelativistic limit of a self-consistent relativistic effective field theory for dynamic problems. It is shown that the standard v/c expansions yields Galilean invariance only to first order in v/c, whereas…
The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of…
We present new aspects of the electromagnetic field by introducting the natural potentials. These natural potentials are suitable for constructing the first order distortions of the metric tensor of Complex Relativity - the theory combining…
We have explored the magnetosphere described by a numerical solution for an axisymmetric rotating field satisfying the force-free and ideal MHD conditions everywhere. The electric current distribution is determined by the requirement of…