Null Electromagnetic Fields Research Articles

Hopf-Ranãda linked and knotted light beam solution viewed as a null electromagnetic field

The Hopf-Ranãda linked and knotted light beam solution, which has been interpreted physically and extended analytically by Irvine and Bouwmeester recently, is viewed in this Letter as a null electromagnetic field. It is shown, in particular, that the Hopf-Ranãda solution is a variant of a luminal null electromagnetic wave due originally to Robinson and Troutman and reported by Bialynicki-Birula recently. This analogy is motivated by means of a method due to Whittaker and Bateman, and a relationship to well-known scalar luminal localized waves is examined.

Cylindrically symmetric Brans–Dicke–Maxwell solutions

We investigate cylindrically symmetric vacuum solutions with both null and non-null electromagnetic fields in the framework of the Brans–Dicke theory and compare these solutions with some of the well-known solutions of general relativity for special values of the parameters of the resulting field functions. We see that, unlike general relativity where the gravitational force of an infinite and charged line mass acting on a test particle is always repulsive, it can be attractive or repulsive for Brans–Dicke theory depending on the values of the parameters as well as the radial distance from the symmetry axis.

SPATIOTEMPORALLY LOCALIZED NULL ELECTROMAGNETIC WAVES I. LUMINAL

Spatiotemporally localized luminal null electromagnetic fields are transverse with respect to the local flow of energy,which is equipartioned between the electric and magnetic fields,and the modulus of their local energy transport velocity equals the speed of light in vacuo. They have vortex structures on planes transverse to the direction of propagation,and,in general,are relatively simple so that explicit calculations can be made of the total energy and the total angular momentum they carry. A class of luminal null electromagnetic waves due originally to Robinson and Troutman is motivated by means of spherical Cunningham and Bateman transformations and their relationships to well-known scalar luminal localized waves are examined. This allows for the introduction of finite-energy localized null luminal electromagnetic waves with spatiotemporal spectra appropriate for applications in diverse physical areas.

Plane-fronted waves in metric-affine gravity

We study plane-fronted electrovacuum waves in metric-affine gravity theories with a cosmological constant. Their field strengths are, on the gravitational side, curvature ${R}_{\ensuremath{\alpha}}^{\ensuremath{\beta}},$ nonmetricity ${Q}_{\ensuremath{\alpha}\ensuremath{\beta}},$ torsion ${T}^{\ensuremath{\alpha}}$ and, on the matter side, the electromagnetic field strength F. Our starting point is the work by Ozsv\'ath, Robinson, and R\'ozga on type N gravitational fields in general relativity as coupled to null electromagnetic fields.

Holonomy groups and spacetimes

A study is made of the possible holonomy group types of a spacetime for which the energy-momentum tensor corresponds to a null or non-null electromagnetic field, a perfect fluid or a massive scalar field. The case of an Einstein space is also included. The techniques developed are, in addition, applied to vacuum and conformally flat spacetimes and contrasted with already known results in these two cases. Examples are given.

Exact solution of the Herrera equation of motion in classical electrodynamics

The Landau–Lifshitz equation is derived as a first-order iteration of the Lorentz–Dirac equation for the charged particle. In those cases with null electromagnetic field’s gradient, the Landau-Lifshitz gives the so named Herrera equation. A general method for the solution of the latter equation is presented and applied to the motion of a particle in a uniform electromagnetic field.

ON THE RELATIONSHIP BETWEEN KILLING-YANO TENSORS AND ELECTROMAGNETIC FIELDS ON CURVED SPACES

The existence of skew symmetric Killing-Yano (KY) tensors of order 2 has been investigated on curved spaces. The integrability conditions of KY tensor including Carter's algebraic relation of symmetric tensor with electromagnetic field have been transcribed in Newman-Penrose formalism. The KY bivectors are classified according to their nullity in electrovac space-times. It is shown that the non-null (or null) electromagnetic field implies to the existence of non-null (or null) KY tensor. Thus Collinson's theorems on the existence of KY tensors on vacuum space-times have been generalized on electrovac space-times. Chandrasekhar's theorem on vacuum type D space-times has also been generalized on the existence of non-null KY tensor on electrovac type D or non-vacuum type D space-time filled with dust. All theorems presented here have been strengthened by giving examples for known space-times. It is also shown that most of KY tensors discussed here are eigen-KY-bivectors of the respective curvature tensors.

Perturbations of solutions of the Einstein–Maxwell equations with a null background electromagnetic field

Expressions for the complete metric and vector potential perturbations of solutions of the Einstein–Maxwell equations with a null background electromagnetic field in terms of two complex scalar potentials are derived using Wald’s method of adjoint operators. The perturbations of the Bell–Szekeres solution, in the regions prior to the collision of the plane-fronted waves, are obtained by this approach. We find that there exist nontrivial u-independent perturbations (where ∂u defines the direction of propagation of the colliding wave) which, when the electromagnetic perturbation vanishes, are exact solutions of the Einstein–Maxwell equations.

Um Modelo Macroscópico para a Força de Reação Radiativa.

We present a simple macroscopic system, a spherical shell with a uniform charge distribution, inside of which we put a test charge. We show that the spherical shell charge distribution, when accelerated, produces a non null electromagnetic field that acts on the test charge i nducing, near the spherical shell center, force such as the Lorentz-Dirac radiation reaction one.

Symmetries of the electromagnetic field in general relativity

Using the null tetrad approach of Newman and Penrose, the symmetries of the electromagnetic fields are investigated. It is found that null electromagnetic fields admit Maxwell collineation, and the existence of Ricci collineation and motion is possible only under certain conditions on the spin-coefficients.

Classical Electromagnetic Radiation in Multidimensional Space-Times

The dependence of various features of electromagnetic radiation on the space-time dimension is investigated. The dimension is d ≥ 4, the lower dimensional theory is not considered. Some features known in four dimensions are carried over (possibly with slight modifications) to extra dimensions, whereas other ones exist only for d = 4. The first group contains, e.g., the notion of null characteristic surfaces and null electromagnetic fields, the geometrical optics approximation ( nearly plane waves), and Fermat′s principle. It turns out that the null rays of the null field are geodesic lines for any dimension (generalization of Mariot′s theorem). The independent functional (algebraic) invariants for a generic electromagnetic field are explicitly constructed, there are [ d/2] of such invariants for d dimensions. A generalized Newman-Penrose formalism (complex Ricci rotation coefficients) is developed in d = 6 and it is used to show that four dimensions are exceptional: only for d = 4 are the rays of a null field shear-free (Robinson′s theorem); in extra dimensions Maxwell′s equations are less restrictive. This formalism is also applied for proving a generalization of Sachs′ optical theorem: for any d, the shadow cast by a small object in a light beam is rotated, expanded, and sheared, but it is not Lorentz contracted.

Bianchi VI cosmological models representing perfect fluid and radiation with electric-type free gravitational fields

A homogeneous Bianchi type VIh cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (γ−1)ɛ is imposed in the particular case of Bianchi VI0 string models. Various physical and kinematical properties of the models are discussed.

Affine collineations in Einstein-Maxwell space-times

The existence of an affine vector field in an Einstein-Maxwell space-time is discussed. We first consider the non-null electromagnetic field case, and show that there are no solutions of the Einstein-Maxwell equations admitting a proper affine collineation. In the case of a null electromagnetic field case, we characterize all the possible solutions with such property.

Petrov type D pure radiation fields of Kundt's class

It is shown that Petrov type D pure radiation fields of Kundt's class can be generated from Kinnersley's B metric. These fields do not admit a null electromagnetic, neutrino or massless scalar field source.

A FAMILY OF SEMI-PLANE-SYMMETRIC ELECTROVACUUM SPACETIMES

It is shown in this paper that the electromagnetic field yielding a semi-plane-symnmetric metric can be either plane-symmetric or semi-plane-symmetric. If it is plane-symmetric, then it must be a non-null electromagnetic field, while if it is semi-plane-symmetric, then it can be either null or non-null. The general solution of semi-plane-symmetric spacetimes yielded by semi-plane-symmetric sourceless null electromagnetic field is also given in this paper.

Completion of plane-symmetric metrics yielded by electromagnetic fields

It is proven that the plane-symmetric metrics associated with the plane-symmetric nonnull electromagnetic fields given by Letelier and Tabensky [2], together with the plane-symmetric metrics associated with the semi-plane-symmetric null electromagnetic fields, given by Li and Liang [3], exhaust the planesymmetric metrics yielded by electromagnetic fields. A “dual interpretation” to the latter metrics, explaining them as being associated with null electromagnetic fields with source, is also given.

Killing vectors and Maxwell collineations in general relativity

The relationship between the symmetries of the gravitational field (Killing vectors) and the symmetries of the electromagnetic field (Maxwell collineations) for electrovac space–times is studied in the context of the Newman–Penrose formalism. Several theorems concerning different kinds of Killing vectors are derived for both null and non-null electromagnetic fields.

Gauge freedom of plane-symmetric line elements with semi-plane-symmetric null electromagnetic fields.

Previously, we gave two classes of plane-symmetric line elements associated with semi-plane-symmetric null electromagnetic fields. Different functions J(V) in those line elements may represent the same geometry. Two criteria on this ``gauge freedom'' are proven in the present paper. The line elements of class B are identified with the conformally flat plane-fronted gravitational waves with parallel rays (pp waves), and the gauge freedom on the function, \ensuremath{\Phi}(v), appearing in the line element of the pp waves is also derived.

On the Robinson theorem and shearfree geodesic null congruences

Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions.

The preferred null symmetries of a null electromagnetic field interacting with a null free gravitational field

The real null vector 1 a of the Newman-Penrose formalism is preferred to correspond to a geometrical symmetry as well as a dynamical symmetry. The 16 types of geometrical symmetries expressed through the vanishing of the Lie derivatives of certain tensor fields with respect to 1 a are examined separately. Two types of dynamical symmetries are imposed simultaneously on 1 a : A null electromagnetic field and a null gravitational field are both chosen to have the same propagation vector 1 a . By adopting freedom conditions on 1 a , it is shown that the symmetries of the null electromagnetic field are shared neither by the free gravitational field nor by the gravitational potentials. In fact the following five preferred null symmmetries are found to be proper: motion, affine collineation, special curvature collineation, curvature collineation, and Ricci collineation. The scalars characterizing the coupled fields are found to be constant with respect to 1 a .