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We present a noncommutative version of a plane-wave solution to the gravitational field equations. We start with a given classical solution, admittedly rather simple, and construct an algebra and a differential calculus which supports the…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in…
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…
We present a general class of noncolinear colliding wave solutions of the Einstein-Maxwell equations given in terms of fourth order polynomials, which in turn can be expressed through Jacobi functions depending on generalized advanced and…
We solve the wave equation for gravitational waves emitted by compact objects systems using the Multipolar Post-Minkowskian (MPM) method, and in the presence of Lorentz invariance violating terms. We select a Lorentz-violating extension of…
This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the…
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
Hyperbolic systems of the first and higher-order partial differential equations appear in many multiphysics problems. We will be dealing with a wave propagation problem in a piece-wise homogeneous medium. Mathematically, the problem is…
Interaction of a charged particle in a static magnetic background, i.e., a Landau system with circularly polarised gravitational wave (GW) is studied quantum mechanically in the long wavelength and low velocity limit. We quantize the…
I find nearly plane-wave solutions for the Gauss-Ampere law for the 4-vector potential, subject to the Lorenz gauge condition, in the spacetime of a plane gravitational plane wave. I assume that the gravitational wave is weak, in the sense…
Previous work has developed the theory of linearized gravitational wave (GW) interactions with matter using the Bondi-Sachs formalism, but with the perturbations restricted to be quadrupolar, i.e., the angular dependence is spherical…
The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in space-time geometry. We show…
We study the many-body problem of charged particles interacting with their self-generated electromagnetic field. We model the dynamics of the particles by the many-body Maxwell-Schr\"odinger system, where the particles are treated quantum…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
We consider a scalar particle in a background formed by two counter-propagating plane waves. Two cases are studied: i) dynamics at a magnetic node and ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations…
We focus on the interaction of a plane gravitational wave with electromagnetic fields and we describe this interaction in the proper detector frame where, thanks to the introduction of Fermi coordinates, it is possible to refer to directly…
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…