Null Electromagnetic Fields Research Articles

Stationary axially symmetric electrovac solutions in the general scalar-tensor theory

A method is presented which reduces the Bergmann-Wagoner-Nordtvedt field equations for a stationary axisymmetric electrovac space-time, to the Einstein-Maxwell equations. In this formalism the solution generation technique of Singh and Rai for Brans-Dicke theory yields a particular class of solutions, for which the conformal scalar field depends upon the radial coordinate only. As an application of the method, new cylindrically symmetric and nonstatic scalar-Maxwell solutions are obtained for null and non-null electromagnetic fields.

Conformally flat null electromagnetic field

A class of conformally flat solutions for null electromagnetic field is presented. Explicit forms of the field tensors are also given. The null field is characterized by shear-free, twist-free, expansion-free, and geodetic null congruences.

LRS Bianchi type-V universes filled with matter and radiation

In this paper we have investigated some LRS Bianchi type-V cosmologicla models representing a viscous fluid distribution with a null electromagnetic field and streaming neutrinos. Various physical and kinematical features of these models have also been explored.

Self-dual Kerr–Schild metrics and null Maxwell fields

A construction for self-dual solutions of Einstein’s equations with metric in Kerr–Schild form from null electromagnetic fields in Minkowski space is described. Two examples are given.

Null electromagnetic fields, total gravitational radiation and collineations in general relativity

The null electromagnetic field, or (F, g, r, S)-structure, and the corresponding Nijenhuis tensor have been studied in an invariant index-free manner. It is seen that the null electromagnetic fields are characterized by the relation F3= 0, and the Nijenhuis tensor plays a very natural role in the study of null electromagnetic fields. The Lichnerowicz contions for the total gravitational radiation have been given in the present setting, and the condition F3=0 has been translated into a corresponding condition on the Ricci tensor. Further, different types of collineations, for (F, g, r, S)-structure, along the propagation and polarization vectors S and T, respectively, have been studied. It is also shown that $$\mathop \pounds\limits_S F_{ij} = 0$$ implies $$F_j^k \mathop \pounds\limits_S g_{ik} = 0$$ . Finally, a covariant conservation law generator has been given for the present structure.

Space spinors

Just as Maxwell’s electromagnetic field equations govern the evolution of electric and magnetic spatial vectors if some choice of time function has been made, so also the neutrino equation and Dirac equation may be understood as governing the evolutions of certain spatial quantities. In this space-plus-time view of the spinor field equations, it is accurate and natural to regard a two-component are written in 3-plus-1 form for both the spinor fields and the corresponding null vector fields. A spatial null vector is of the form M=E+iB, with E⋅E−B⋅B=0=E⋅B, so it is also of the correct algebraic form for describing a null electromagnetic field. The time derivative of a squared neutrino field Ma, however, is -i curl Ma+〈M〉cDaMc, compared with simply -i curl Ma for a source-free Maxwell field. Here 〈M〉c is the real spatial unit vector in the neutrino propagation direction E×B, and Da is the spatial covariant derivative.

On rotating plane-fronted waves and their Poincaré-invariant differential geometry

After reviewing the rotating plane-fronted wave type solutions of the scalar wave equation and Maxwell’s vacuum equations in flat space (we point out that there are Yang–Mill analogs as well), we study their Poincaré-invariant geometry by discussing their characteristic differential invariants and a noninertial curvilinear coordinate system canonically associated with them. In one of the appendices we treat the shearfree and the nondiverging null hypersurfaces in complex Minkowski space, in another one we derive the Yang–Mills version of Robinson’s theorem on null electromagnetic fields.

Null electromagnetic fields in the generalized Einstein–Maxwell field theory

In this paper solutions to the source-free generalized Einstein–Maxwell field equations with a null electromagnetic field are investigated. It is argued that the principal null congruence of the null electromagnetic field need not be geodesic, shear-free or a repeated principal null congruence of the gravitational field. However, if the principal null congruence of the null electromagnetic field is geodesic and shear-free, then it is shown that it must be hypersurface orthogonal, expansion-free, and a repeated principal null congruence of the gravitational field. The local form of all such solutions of Petrov type III or N is presented.

A class of axisymmetric stationary exact solutions of Einstein-Maxwell equations

Einstein-Maxwell vacuum field equations of an axially symmetric stationary charged rotating source are studied. A class of asymptotically flat solutions representing the exterior field of a stationary rotating charged oblate spheroidal source is obtained. By examining eigenvectors of Einstein tensor Gij, invariants RijRij and Petrov classification of Weyl's conformal tensor, it is proved that the metric potentials describe null electromagnetic fields.

Tilting and viscous models in a class of Type VI/0/ cosmologies

view Abstract Citations (27) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Tilting and viscous models in a class of type VI0 cosmologies. Dunn, K. A. ; Tupper, B. O. J. Abstract The class of Type VI(0) cosmological models with perfect fluid and electromagnetic field which were investigated in a previous article is shown to contain tilting models which have zero pressure and a null electromagnetic field. It is also shown that the class contains viscous fluid models which are necessarily nontilting. Properties of these models are discussed. Publication: The Astrophysical Journal Pub Date: June 1978 DOI: 10.1086/156154 Bibcode: 1978ApJ...222..405D Keywords: Astronomical Models; Cosmology; Electromagnetic Fields; Viscous Fluids; Attitude (Inclination); Electrical Resistivity; Ideal Fluids; Kinematics; Mathematical Models; Astrophysics; Cosmological Models full text sources ADS |

On the invariance transformations of the energy-momentum tensor in the Einstein-Maxwell theory

A homothetic conformal transformation of the metric tensor is both necessary and sufficient to ensure that a source-free non-null electromagnetic field in four dimensions undergoes a duality rotation leaving its energy-momentum tensor invariant. For null electromagnetic fields the condition is sufficient but not necessary. The result suggests that vacuum Einstein-Maxwell space-times exist which admit groups of homothetic motions. If the order of such a group is greater than unity it must be associated with isometry transformations of the metric tensor other than those obtained as a special case of the conformal group.

Plane wave solutions in scalar tensor theories and solutions of source-free Einstein–Maxwell theory

Vacuum solutions of the field equations that satisfy the original notion of the plane wave, namely gμν=gμν(Z), Z=Σμaμxμ, aμ’s being constants and gμνZ,μZ,ν=0, are sought for both Brans–Dicke scalar–tensor theory and the more recent scalar–tensor theory due to Sen and Dunn. (Here Greek letters range from 1 to 4 and Latin letters from 1 to 3.) A complete set of solutions are obtained for both cases. Although not required at the outset, it turns out that, in both cases, the scalar field is also function of Z alone. As a by-product, one gets the complete set of solutions of the Einstein–Maxwell equations for the null electromagnetic field for the cases when gμν satisfies the above-mentioned requirement.

The collision of plane waves in general relativity

A number of exact solutions of Einstein's equations are obtained, which describe the collision and subsequent interaction of two plane parallel waves. Gravitational waves, null electromagnetic fields, and neutrino fields are all considered with collisions between any two types. It is shown that two such waves mutually focus each other with the focus usually appearing as a singularity in space-time. Further conclusions are made regarding the qualitative nature of the interactions, and it is argued that these also apply in more realistic physical situations.

Symmetries and the Einstein-Maxwell field equations the null field case

This paper deals with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. The electromagnetic field is assumed to be null. It is proved that if the space-time admits a group of isometrics then the fluid velocityui, energy densityμ, pressurep, and charge densitye are invariant under the group. In addition, if the charge density is nonzero, the electromagnetic field tensorfij is also invariant. On the other hand, examples of exact solutions are given which establish that ife = 0, thenFij is not necessarily invariant under the group. In the case of spherically symmetric space-times, however, in which the group of isometries acting isSO (3),fij is invariant, independently of whether or note is nonzero. This result leads to the conclusion that in a spherically symmetric space-time the field equations in question admit no solutions with non-trivial null electromagnetic field.

Ricci and Maxwell collineations in a null electromagnetic field

It has been shown that Synge's metric representing null electromagnetic field admits proper Ricci collineation. The space-time admits curvature collineation in special cases and the CC vectors are obtainable from the RC vector by an appropriate choice of the arbitrary quantities involved. When the RC vector is constrained to give motion the space-time permits 5-, 6- and 7-parameter groups of motions in the different cases considered. It is found that the space-time admits Maxwell and Ricci collineations along common directions in special cases for which both the conservation laws are satisfied.

Conformally flat solutions of the Einstein−Maxwell equations for null electromagnetic fields

The spin coefficient formalism of Newman and Penrose is employed to obtain a direct derivation of the most general conformally flat solution of the source−free Einstein−Maxwell equations for null electromagnetic fields.

Null electromagnetic fields in spaces of high symmetry

The paper investigates the solutions of Maxwell-Einstein equations for null electromagnetic fields with or without matter in case of spaces of high symmetry. For the spherically symmetric space no such solution exists, while for cylindrically symmetric spaces, there arises a wide variety of situations. In reality, for the solutions that emerge, the spaces should more appropriately be termed plane symmetric. Some solutions are exhibited.

Null electromagnetic fields in general relativity

The necessary and sufficient condition that a general Riemannian space-time $$ds^2 = g_{ij} dx^i dx^j$$ , may represent a null electromagnetic field is S = C, where $$S = R_{hijk} F^{hi} F^{jk} ,C = C_{hijk} F^{hi} F^{jk} .$$ .

Partons and gravitation: Some puzzling questions

The rather general belief in the theory of gravitation according to which neutral massive bodies with zero electric and magnetic moments are surrounded by a null electromagnetic field is analyzed from a critical viewpoint. Beginning the analysis at an atomic level, it is not difficult to see that neutral atoms are surrounded by a nonnull electromagnetic field generated by their peripheral electrons and by their nuclei even though their overall charge is zero. The data emerging from recent deep inelastic e-p scattering experiments clearly indicate that nucleons are composed by a number of charged constituents, often called partons, in a highly dynamical behavior. Consequently, nucleons and nuclei can also be a rather relevant source of electromagnetic field, in view of the presumed large number of partons, which is produced not only by their overall charges, but more properly by the charges of their individual constituents. Summing up the contributions from a large number of atoms, the possibility of a seizable electromagnetic field surrounding any neutral massive body emerges. Three assumptions, termed standard, weak, and strong according to which the energy-momentum tensor of the electromagnetic field generated by the matter constituents does not contribute, or partially contribute, or is entirely responsible of the gravitational field, are introduced. In order to assess the physical relevance of each of the above assumptions, a simple bound state model of the π 0 particle is introduced in terms of two charged valence partons in a 1S state. Some models of the electromagnetic field produced by the π 0 charged constituents are derived as a ground for further extension to the case of nucleons, nuclei, and entire atoms. The gravitational field equations for the π 0 particle according to the standard assumption are recalled and the ones according to the weak and strong assumptions are introduced. The puzzling implications of our analysis clearly cast shadows on the standard assumption, leaving as possible alternative for an exact formulation a selection between the weak and the strong assumptions. Some implications of the latter assumptions are discussed; the restrictions for the exterior case are derived using the framework of the “already unified theory”; some inconsistency with the gravitational wave theory is briefly discussed; and it is emphasized that the strong assumption implies a fully geometrical unification of gravitational and electromagnetic fields since the gravitational field is identified with a particular form, or “mutation,” of the electromagnetic field originated primarily in the nuclear, but also in the atomic structure. The admissibility of both the weak and the strong assumptions on the basis of our present knowledge is discussed and the feasibility of some experiments aiming at the proper selection as well as the ultimate physical assessment of the new assumptions is briefly analyzed.

Spherically symmetric solutions of Einstein-Maxwell theory with null fluid

Solutions of the Einstein-Maxwell equations with the addition of terms representing charged null fluid emitting from a spherically symmetric body are found. One type of solution is a simple extension of that found by Bonnor and Vaidya while the other represents a null electromagnetic field with null electric current.