Source-free Electromagnetic Field Research Articles

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν; the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

Wormhole solutions sourced by fluids, I: Two-fluid charged sources

We briefly discuss some of the known and new properties of rotating geometries that are relevant to this work. We generalize the analytical method of superposition of fields, known for generating nonrotating solutions, and apply it to construct massless and massive rotating physical wormholes sourced by a source-free electromagnetic field and an exotic fluid both anisotropic. Their stress-energy tensors are presented in compact and general forms. For the massive rotating wormholes there exists a mass-charge constraint yielding almost no more dragging effects than ordinary stars. There are conical spirals through the throat along which no local negative energy densities are noticed for these rotating wormholes. This conclusion extends to nonrotating massive type I wormholes derived previously by the author that seem to be the first kind of nonrotating wormholes with this property. Based on the classification made in J. Cosmol. Astropart. Phys. 07 (2015) 037 [arXiv:1412.8282]: "Type I wormholes have their radial pressure dying out faster, as one moves away from the throat, than any other component of the stress-energy and thus violate the least the local energy conditions. In type II (resp. III) the radial and transverse pressures are asymptotically proportional and die out faster (resp. slower) than the energy density".

Unified Theories of Gravitational and Electromagnetic Fields in Riemannian Geometry and Higher Dimension

Some unified theories on the gravitational and electromagnetic fields are researched. We investigate mainly two new geometric unified theories. A method is that the gravitational field and the source-free electromagnetic field can be unified by the equations Rklmi = κTklmi* in the Riemannian geometry, both are contractions of im and ik, respectively. If Rklmi = κTklmi* =constant, it will be equivalent to the Yang’s gravitational equations Rkm;l –Rkl;m = 0, which include Rlm= 0. From Rlm= 0 we can obtain the Lorentz equations of motion, the first system and second source-free system of Maxwell’s field equations. This unification can be included in the gauge theory, and the unified gauge group is SL(2,C) × U(1)=GL(2,C), which is just the same as the gauge group of the Riemannian manifold. Another unified method on the general nonsymmetric metric field with high-dimensional space-time and its matrix representations are analyzed mathematically. Further, the general unified theory of five-dimensional space-time combined quantum theory and four interactions is researched. Some possible unification ways on the gravitational and electromagnetic fields are discussed. The general matrix and various corresponding theories may decompose to a sum of symmetry and antisymmetry. Moreover, we proposed an imaginative representation on the ten dimensional space-time.

Conserved matter superenergy currents for orthogonally transitive Abelian G2 isometry groups

In a previous paper we showed that the electromagnetic superenergy tensor, the Chevreton tensor, gives rise to a conserved current when there is a hypersurface orthogonal Killing vector present. In addition, the current is proportional to the Killing vector. The aim of this paper is to extend this result to the case where we have a two-parameter Abelian isometry group that acts orthogonally transitive on non-null surfaces. It is shown that for four-dimensional Einstein–Maxwell theory with a source-free electromagnetic field, the corresponding superenergy currents lie in the orbits of the group and are conserved. A similar result is also shown to hold for the trace of the Chevreton tensor and for the Bach tensor, and also in Einstein–Klein–Gordon theory for the superenergy of the scalar field. This links up well with the fact that the Bel tensor has these properties and it gives further support to the possibility of constructing conserved mixed currents between the gravitational field and the matter fields.

Orthogonality relations for triple modes at dielectric boundary surfaces

Abstract We work out the orthogonality relations for the set of Carniglia-Mandel triple modes which provide a set of normal modes for the source-free electromagnetic field in a background consisting of a passive dielectric half-space and the vacuum, respectively. Owing to the inherent computational complexity of the problem, an efficient strategy to accomplish this task is desirable, which is presented in the paper. Furthermore, we provide all main steps for the various proofs pertaining to different combinations of triple modes in the orthogonality integral.

Orthogonality relations for triple modes at dielectric boundary surfaces

We work out the orthogonality relations for the set of Carniglia-Mandel triple modes which provide a set of normal modes for the source-free electromagnetic field in a background consisting of a passive dielectric half-space and the vacuum, respectively. Owing to the inherent computational complexity of the problem, an efficient strategy to accomplish this task is desirable, which is presented in the paper. Furthermore, we provide all main steps for the various proofs pertaining to different combinations of triple modes in the orthogonality integral.

The angular spectrum representation and the Sherman expansion of pulsed electromagnetic beam fields in dispersive, attenuative media

The angular spectrum of plane-waves representation of a pulsed electromagnetic beam field propagating in a dispersive, attenuative medium occupying the half-space expresses that wave field as a superposition of both homogeneous and inhomogeneous plane waves. A generalization of the Sherman expansion for source-free wave fields in lossless media to the lossy, dispersive medium case is used to derive a spatial series representation of a pulsed, source-free electromagnetic beam field from its angular spectrum representation. This spatial series representation displays the temporal evolution of the pulsed beam field explicitly through a single-contour integral that is of the same form as that obtained in the Fourier-Laplace description of a pulsed plane-wave field that is propagating in the positive z-direction in the lossy, dispersive medium. The temporal pulse evolution is found to depend upon the transverse spatial position in the beam field through the derivatives of the field boundary values.

Alternative potentials for the electromagnetic field

The source-free electromagnetic field can be expressed in terms of two complex potentials α,β, which are related to the Debye potentials. The potentials {α,β} corresponding to various fields are discussed. A conserved radiation density ρ can be constructed in terms of these potentials, this density is positive (negative) for positive (negative) helicity radiation.

Algebraic Programming in the Hamiltonian Treatment of the Einstein–Maxwell Equations

We present new procedures in REDUCE language using the EXCALC package (adapted for IBM-PC machines) for algebraic programming in the hamiltonian formulation of Einstein–Maxwell equations. The dynamic and the constraint equations containing specific terms of the interaction of gravity with source-free electromagnetic field are translated into computer procedures. The results obtained by processing some examples of space-time models are presented.

Exact bianchi type-II, VIII, and IX cosmological models with matter and electromagnetic fields in Lyra's manifold

Spatially-homogeneous and anisotropic Bianchi type-II, VIII, and IX stiff-fluid cosmological models in the presence of source-free electromagnetic fields are obtained in Lyra's manifold. Some properties of the models are also discussed.

Bianchi type-II, VIII, and IX cosmological models with matter and electromagnetic fields

We present analytic solutions of the Einstein-Maxwell equations for cosmological models of LRS Bianchi type-II, VIII, and IX. The solutions represent anisotropic universes with source-free electromagnetic fields and perfect fluids matter satisfying the equation of state that is a function of the cosmic-time. Some physical properties of the models have been discussed.

Third-order geometrical null symmetries of gravitational fields

The first-, the second-, and the third-order null Killing vectors in a gravitational field are explored separately. When an algebraically special Petrov-type free gravitational field isaligned with a source-free (nonnull/null) electromagnetic field, their common propagation vectorl a is shown to be a third-order null Killing vector field (ℒ l ℒ l ℒ l g ab = 0,ℒ l ℒ l g ab ≠ 0). When the two fields arenot aligned, the necessary and sufficient conditions for the existence of a third-order null symmetry are obtained in Newman-Penrose formalism.

Source-free electromagnetic fields in the Einstein-G�del universe

A metric containing a parameter e (e2 = 1) has been derived which represents axially symmetric source-free electromagnetic fields in a static Einstein universe when e is put equal to 1. The same metric represents the source-free electromagnetic fields in a Godel rotating universe when e is put equal to-1. Many known solutions are obtained as particular cases.

Canonical and duality transformations for the electromagnetic field

In earlier papers we have given a new hamiltonian formulation of the source-free electromagnetic field. In this paper we show that the most general linear canonical transformation with constant coefficients which leaves the form of the field equations and the hamiltonian invariant is the duality transformation. Other invariant quantities of physical interest are also discussed.

Radiating Demianski-type metrics and the Einstein-Maxwell fields

AbstractA Demianski-type metric is investigated in connection with the Einstein-Maxwell fields. Using complex vectorial formalism, some exact solutions of Einstein-Maxwell field equations for source-free electromagnetic fields plus pure radiation fields are obtained. The radiating Demianski solution, the Debney-Kerr-Schild solution and the Brill solution are derived as particular cases.

The Vaidya–Patel solution with Robertson–Walker metric as a rotating inflationary scenario

The Vaidya–Patel solution of a rotating homogeneous fluid in the presence of a Maxwellian source-free electromagnetic field is interpretated as an inflationary scenario with a gauge field with local U(1) symmetry, a vacuum energy, and a rotating perfect fluid. An explicit solution is found to be expressible in terms of known solutions representing the radiation filled Robertson–Walker universe with a cosmological term. In the case that the rotating fluid is radiation, the discussion of the model is considerably simplified. How the time scale of transition into a pseudo-de Sitter stage, as observed by an observer following the rotating fluid, is affected by vorticity is also studied.

Some properties of Hertz vectors for source-free electromagnetic fields

Abstract In this paper we discuss some properties of solutions of the Hertz equation for source-free electromagnetic fields. First we give an operational form of the solution at any time in terms of the field at a particular time. Then we discuss the use of the Hertz equation to obtain conservation laws for various expressions involving the field vectors. Finally we discuss the variational formulation of the Hertz equation giving a Lagrangian and two possible Hamiltonians.

Nonexistence of static conformally-flat solutions in self-creation cosmology

It is shown that there do not exist spherically-symmetric conformaly-flat static solutions, in the self-creation cosmology proposed by Barber, representing disordered radiation and in the presence of source-free electromagnetic field except for the trivial empty flat space-time of Einstein's theory. The solution in the vacuum case is also only a flat space time of Einstein's theory.

Hertz and Debye potentials and electromagnetic fields in general relativity

In this paper the authors extend earlier work on the application of curved space Hertz and Debye bivector potentials to the solution of Maxwell's equations for source-free electromagnetic test fields in general relativity. They classify all Hertzian schemes by considering bivector potentials which are eigenvectors of the Hodge duality operator. This approach has the advantage of simplifying the task of solving the system of coupled equations which determine the Hertz potential. They then apply their results to several Debye schemes and present a new scheme which can be used in Petrov type-D spacetimes. For each of these schemes, the one-component wave equation for the potential is given with respect to the null tetrad/Newman-Penrose formalism and, for the first time, with respect to an orthonormal basis.

Bianchi type V perfect fluid models with source-free electromagnetic fields

The Einstein-Maxwell Field equations characterizing a nontitled Bianchi type V perfect fluid model with source-free electromagnetic field are solved exactly in the nonlocally rotationally symmetric case. It is found that these equations admit one and only one exact solution, expressible, however, in terms of two arbitrary functions.