Related papers: Electrovac $pp$-waves
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
We present new exact inhomogeneous vacuum cosmological solutions of Einstein's equations. They provide new information about the nature of general cosmological solutions to Einstein's equations.
We derive an asymptotic solution of the Einstein field equations which describes the propagation of a thin, large amplitude gravitational wave into a curved space-time. The resulting equations have the same form as the colliding plane wave…
I present a new method to generate rotating solutions of the Einstein--Maxwell equations from static solutions, and briefly discuss its general properties.
We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some…
The formulation of the Einstein field equations admitting two Killing vectors in terms of harmonic mappings of Riemannian manifolds is a subject in which Charlie Misner has played a pioneering role. We shall consider the hyperbolic case of…
We find an {\it exact} pp--gravitational wave solution of the fourth order gravity field equations. Outside the (delta--like) source this {\it not} a vacuum solution of General Relativity. It represents the contribution of the massive,…
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton-Jacobi equation for a test particle is integrated by the method of complete separation of variables with…
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an…
We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(\boldsymbol{g},\boldsymbol{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of…
The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes $(M,g,h\, dvol_g)$ of dimension 4, where the underlying manifold $(M,g)$ is a $pr$-wave. We use this result to provide examples of…
A new class of solutions to the coupled, spherically symmetric Einstein-Maxwell equations for a compact material source is constructed. Some of these solutions can be made to satisfy a number of requirements for being physically relevant,…
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…
An exact solution of the current-free Einstein-Maxwell equations with the cosmological constant is presented. The solution is of Petrov type D, includes the negative cosmological constant, and could be a ``background addition'' to the…
Characterizing electromagnetic wave propagation in nonlinear and inhomogeneous media is of great interest from both theoretical and practical perspectives, even though it is extremely complicated. In fact, it is still an unresolved issue to…
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…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…