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We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the…
In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G(VII) is completed. All non-equivalent exact…
We present plane-wave-type solutions of the lowest order superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a stringy generalization of the Brinkmann metric. Some…
We propose a new set of BMS charges at null infinity, characterized by a super-translation flux that contains only the `hard' term. This is achieved with a specific corner improvement of the symplectic 2-form, and we spell the conditions…
In an attempt to clarify what is the velocity of a particle in doubly special relativity, we solve Maxwell's equations invariant under the position-space nonlinear Lorentz transformation proposed by Kimberly, Magueijo, and Medeiros. We show…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
The purpose of this paper is to present mathematical evidence that electromagnetic near-field waves and wave groups, generated by an oscillating electric dipole, propagate much faster than the speed of light as they are generated near the…
Maxwell's equations are modified to incorporate a scalar field to account for the London's superconductivity. Assuming the electromagnetic field is described by the Klein-Gordon equation, London's equations of superconductivity are then…
We consider the axion field and electromagnetic waves with rapid time dependence, coupled to a strong time independent, asymptotically approaching a constant at infinity "mean" magnetic field, which takes into account the back reaction from…
In this paper the fields generated by an electric dipole and a gravitational quadrapole are shown to propagate superluminally in the nearfield of the source and reduce to the speed of light as the fields propagate into the farfield. A…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
The computation of the emitted radiation by an accelerated external particle can be addressed in a gauge theory with the insertion of a Wilson loop. With the addition of conformal symmetry this problem is consistently formalized in terms of…
In this work we investigate the presence of electrically charged structures that are localized in two and three spatial dimensions. We use the Maxwell-scalar Lagrangian to describe several systems with distinct interactions for the scalar…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
Maxwell's equations are invariant under both duality rotations and conformal transformations. Recently Bandos, Lechner, Sorokin, and Townsend have found a nonlinear generalisation of electrodynamics which possesses both of these symmetries.…
A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's…
We extend the derivation of mass formulas for stationary axisymmetric asymptotically locally flat solutions with string singularities on the polar axis to general supergravity actions containing vector and scalar fields. It is based on the…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…