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We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
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…
Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…
Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved…
The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive…
Geometric optics effectively describes the propagation of electromagnetic waves when the wavelength is much smaller than the characteristic length scale of the medium, making wave phenomena like diffraction negligible. As a result, light…
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that…
Electromagnetic waves propagating in the background provided by a spacetime hosting a strong curvature, naked singularity, are fully studied. The analysis is performed not only in the realm of geometrical optics -- which, not surprisingly,…
We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For…
The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $\omega(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and…
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…
The wavelength and the propagation length of the edge magnetoplasmons, running along the edge of a two-dimensional electron layer in a semiconductor quantum-well structure are theoretically studied as a function of frequency, magnetic…
Gravitational waves travel through the distributions of matter and dark energy during propagation. For this reason, gravitational waves emitted from binary compact objects serve as a useful tool especially to probe the nature of dark…
Interesting phenomena and problems arising from the coupling of large-scale electromagnetic fields and spacetime curvature, are introduced and studied within this thesis. From electromagnetic wave propagation in curved spacetime to…
In this paper, the axion contribution to the electromagnetic wave propagation is studied. First we show how the axion electrodynamics model can be embedded into a premetric formalism of Maxwell electrodynamics. In this formalism, the axion…
This paper is intended to investigate the relation between electrodynamics in anisotropic material media and its analogous formulation in an spacetime, with non-null Riemann curvature tensor. After discussing the electromagnetism via chiral…
A new method to find the propagation equation system governing the scattering of an electromagnetic wave by a nonlinear medium is proposed. The aim is to let the effects appear spontaneously, deleting as far as possible the phenomenological…
We investigate the propagation of the gravitational waves in a cosmological background. Based on the framework of spatially covariant gravity, we derive the general quadratic action for the gravitational waves. The spatial derivatives of…
As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has been increasingly paid attention to in the past decade. Here, in light of Huygens-Fresnel principle, we propose a theoretical frame to study…
It is demonstrated that the propagation of electro-magnetic waves in an appropriately designed wave-guide is (for large wave-lengths) analogous to that within a curved space-time -- such as around a black hole. As electro-magnetic radiation…