Related papers: Knots and the Maxwell Equations
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
In general relativity, Maxwell's equations are embedded in curved spacetime through the minimal prescription, but this could change if strong-gravity modifications are present. We show that with a nonminimal coupling between gravity and a…
We present analytic solutions of Maxwell equations for infinitely long cylindrical conductors with nonvanishing electric charge and currents in the external background spacetime of a line gravitomagnetic monopole. It has been shown that…
We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…
The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined covariantly. More precisely, two…
We investigate the cylindrical class of Newman Tamburino equations in the presence of an aligned Maxwell field. After obtaining a complete integration of the field equations we look at the possible vacuum limits and we examine the…
We derive an alternative formulation of the field equations for macroscopic electromagnetic fields in a linear magneto-dielectric medium as an identity of the Maxwell--Minkowski equations, complementing a variety of other representations…
We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative…
After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological…
We construct a new class of charged rotating black string solutions coupled to a nonlinear electromagnetic field in the background of anti-de Sitter spaces. We consider two types of nonlinear electromagnetic field namely, logarithmic and…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.
The class of static solutions found by Gibbons and Wells for dilaton-electrodynamics in flat spacetime, which describe nontopological strings and walls that trap magnetic flux, is extended to a class of dynamical solutions supporting…
It is shown that electro (magneto) static sector of Maxwell's electrodynamics coupled to the dilaton field in a string theory form possesses the symmetry group of the stationary General Relativity in vacuum. Performing the Ernst formalism,…
On the basis of the ordinary mathematical methods we discuss new classes of solutions of the Maxwell's equations discovered in the papers by D. Ahluwalia, M. Evans and H. M'unera et al.
In this paper, we investigate the thermodynamics of dyonic black holes in the presence of Born-Infeld electromagnetic field. We show that electric-magnetic duality reported for dyonic solutions with Maxwell field is omitted in case of…
We show that a reformulation of the ADM equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate…
A simple relation between the Maxwell system and the Dirac equation based on their quaternionic reformulation is discussed. We establish a close connection between solutions of both systems as well as a relation between the wave parameters…
We construct new solutions of the vacuum Einstein field equations with multiple NUT parameters, with and without cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat.…