Related papers: Maxwell's equations with hypersingularities at a n…
We consider Maxwell fields associated with any shear-free null geodesic congruence on Minkowski or Riemannian background space-time. Bounded singular loci of these fields are treated as particle-like formations, possess "self-quantized"…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $\Omega$ with an analytic boundary $\Gamma$, on which we impose impedance boundary conditions. We…
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…
In this paper, I develop the Soldering formalism in a new domain - the noncommutative planar field theories. The Soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into…
A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce…
We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with…
In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete, if the electromagnetic parameters $\eps, \, \mu,…
We present a novel family of asymptotically Schrodinger hyperscaling violating black holes with a generic dynamical critical exponent and an arbitrary number of spacetime dimensions. This black hole family represents a solution within the…
The conventional decomposition of a vector field into longitudinal (potential) and transverse (vortex) components (Helmholtz's theorem) is claimed in [1] to be inapplicable to the time-dependent vector fields and, in particular, to the…
It is shown that Maxwell's equations in media without source can be written as a contact Hamiltonian vector field restricted to a Legendre submanifold, where this submanifold is in a fiber space of a bundle and is generated by either…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
A transparent linear magneto-dielectric material in free space that is illuminated by a finite quasimonochromatic field is a thermodynamically closed system, definitively, regardless of what field and material subsystems that one defines.…
Recently a new formalism for perturbations of Maxwell's equations on the background of the Kerr-NUT-(A)dS spacetime was proposed, with which the equations are reduced to a equation of motion of a scalar field that can be solved by…
The solutions of $U(1)$ gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The…
We study the static, spherically symmetric black hole solutions for a non-minimally coupled multi-scalar theory. We find numerical solutions for values of the scalar fields when a certain constraint on the maximal charge is satisfied.…
We investigate the passivity constraints on the relations between transmission, reflection, and absorption eigenvalues in linear time-invariant systems. Using techniques from matrix analysis, we derive necessary and sufficient conditions…
We analyse the Maxwell's spectrum on thin tubular neighborhoods of embedded surfaces of $\mathbb R^3$. We show that the Maxwell eigenvalues converge to the Laplacian eigenvalues of the surface as the thin parameter tends to zero. To achieve…
We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…