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The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
The unified field is a Maxwell-Lorentz field. Maxwell-Lorentz equations for potentials in standard four-dimensional form are satisfied exactly. This is achieved by involving new fundamental field sources, strict definition of which requires…
The system of Maxwell equations with an initial condition in a vacuum is solved in a cylindrical coordinate system. It derives the cylindrical transverse electromagnetic wave mode in which the electric field and magnetic field are not in…
Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
The usual Helmholtz decomposition gives a decomposition of any vector valued function into a sum of gradient of a scalar function and rotation of a vector valued function under some mild condition. In this paper we show that the vector…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
We consider source-free electromagnetic fields in spacetimes possessing a non-null Killing vector field, $\xi^a$. We assume further that the electromagnetic field tensor, $F_{ab}$, is invariant under the action of the isometry group induced…
A robust and efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector Helmholtz…
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…
Maxwell's equations are solved when the amplitude and phase of the electromagnetic field are determined at all points in space. Generally, the Stokes parameters can only capture the amplitude and polarization state of the electromagnetic…
Electromagnetic waves arise in many area of physics. Solutions are difficult to find in the general case. In this paper, we numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Straightforward finite difference…
We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined…
The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent…
Considering two static, electrically charged, elementary particles, we demonstrate a possible way of proving that all known fundamental forces in the nature are the manifestations of the single, unique interaction. We re-define the gauging…
Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the…
In this paper, we explore the existence of various non-singular compact stellar solutions influenced by the Maxwell field within the matter-geometry coupling based modified gravity. We start this analysis by considering a static spherically…
Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and…