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We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is…
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…
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…
Electromagnetism is the energy originating from an electric charge. Our purpose is to enlarge Maxwell. Include the charge transfer phenomenology. A four bosons electromagnetism is derived. An EM completeness is achieved. The charge's set…
A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be…
In this paper the macroscopic Einstein and Maxwell equations for system, in which the electromagnetic interactions are dominating (for instance, the cosmological plasma before the moment of recombination), are derived. Ensemble averaging of…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
Within the context of a $5D$ space-time, we construct a unified theory of gravity and electromagnetism from which the Einstein field equations and Maxwell equations emerge, with homogenous Maxwell equations appearing naturally. We also…
In the Relativistic Quantum Geometry (RQG) formalism recently introduced, was explored the possibility that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to…
The article describes a new approach to obtaining the energy-momentum tensor of electromagnetic field in medium without the use of Maxwell's equations and Poynting theorem. The energy-momentum tensor has new qualities and consequences. Its…
In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's…
Suggested non-linear, non-gauge modification of the Maxwell theory of electromagnetism based on correlation between electromagnetic potential, $A_a$, and metric, $g_{ab}$, such that tensor $G_{ab} = g_{ab} - l^2{A}_a{A}_b$ represents…
We investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there…
Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…
The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…