Related papers: Space-time orientations and Maxwell's equations
We present a gauge invariant generalization of Maxwell's equations and p-form electromagnetism to Kaehler spacetimes.
A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\'{}s field equations. The extension consists in the use of a six dimensional…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
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 derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the…
In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that the time dependence of the permittivity gives rise to…
Maxwell's equation, Dirac's equation and the equation of gravito-electromagnetism are shown to be particular instances of the extended Maxwell system. The equations are discussed in the framework of the theory of evolutionary equations.…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure…
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…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
Two questions connected to the macroscopic Maxwell equations are addressed: First, which form do they assume in the hydrodynamic regime, for low frequencies, strong dissipation and arbitrary field strengths. Second, what does this tell us…
Two theorems are proved concerning how stationary axisymmetric electrovac spacetimes that are equatorially symmetric or equatorially antisymmetric can be characterized correctly in terms of the Ernst potentials $\E$ and $\Phi$ or in terms…
We construct an analytic solution to Maxwell's equations that violates global charge conservation, by building on the possibilities demonstrated in [Foundations of Physics 49, 330 (2019)]. The construction is valid for a spacetime…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
In this work, we derive two formulas encoding the polarization direction and luminosity of synchrotron radiations from the moving electrons in curved spacetime under the geometric optics approximation. As an application, we further study…
Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
The Riemann -- Silberstein -- Majorana -- Oppengeimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation…
Many papers have been published over the years that either conjecture or even (claim to) prove the universality of the form of Maxwell's equations. We present yet another derivation of Maxwell's equations and discuss the conclusions…