Electromagnetic interpretation of the massless spin-1 field equation in curved space-time

The source-free Maxwell equations associated to the massless spin-1 free field equation are considered in curved space-time. The gauge invariance of the theory is discussed by using as starting point the notion of the spinor potential. The structure of the electromagnetic field in the case of the Robertson-Walker space-time is discussed by using the solutions of the massless spin-1 equations previously determined. The flat-universe case of the standard cosmology is studied exactly and considered in some limiting physical situations.     

Riemannian-Maxwellian invertible structures in general relativity

It is shown that a space-time admitting a nonsingular 2-form satisfying the source-free Maxwell equations and a Lorentzian involution under which the 2-form and the exterior derivative of a related 2-form are skew invariant while the trace-free Ricci tensor and the covariant derivative of the involution itself are invariant possesses locally an invertible 2-parameter Abelian isometry group with nonsingular orbits.On sabbatical leave from the Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada.     

On the role of the Killing tensor in the Einstein-Maxwell theory

It is shown that when a four dimensional source-free Einstein-Maxwell space-time admits a group of motions leaving the electromagnetic field unchanged a linear relation exists between two Maxwell fields and the covariant derivative of a Killing vector. For the case in which the two electromagnetic fields are related by a duality rotation it is seen that a purely geometric form of Einstein's equations may be derived. The behaviour of these under a class of quasi conformal transformations of the metric is shown to lead to Harrison's theorem.     

Gravitation and Electrodynamics over SO(3,3)

In a series of papers, an approach to field theory is developed in which matter appears by interpreting source-free (homogeneous) fields over a 6-dimensional space of signature (3,3), as interacting (inhomogeneous) fields in space-time. The extra dimensions are given a physical meaning as coordinatized matter. The inhomogeneous energy-momentum relations for the interacting fields in space-time are automatically generated by the simple homogeneous relations in 6-d. We then develop a Weyl geometry over SO(3,3) as base, under which gravity and electromagnetism are essentially unified via an irreducible 6-calibration invariant Lagrange density and corresponding variational principle. The Einstein–Maxwell equations are shown to represent a low-order approximation, and the cosmological constant must vanish in order that this limit exist.     

Comments on the unification of electromagnetism and gravitation through “Generalized Einstein manifolds”

Akbar-Zadeh [J. Geom. Phys. 17 (1995) 342] has recently proposed a new geometric formulation of Einstein-Maxwell system with source in terms of what are called “Generalized Einstein manifolds”. We show that, contrary to the claim, Maxwell equations have not been derived in this formulation, and that the assumed equations can be identified only as source-free Maxwell equations in the proposed geometric setup. A genuine derivation of source-free Maxwell equations is presented within the same framework. We draw a conclusion that the proposed unification scheme can pertain only to source-free situations.     

Generalized Klein–Gordon field equations with octonion space-time (OST) algebra

The concept of space-time representation is redefined using the octonion space-time (OST) algebra. In this study, describing the properties of octonions and their possible connection with Euclidean space-times, the internal and external space-time events are represented within the OST algebra. Keeping in mind the octonionic dual-Euclidean space-times, we express the homogeneous field equations which leads to the symmetrical nature of internal and external space-times. We derive the generalized Proca–Maxwell equations for massive-dyons in the case of the OST algebra. Accordingly, we have obtained a new set of octonionic Klein–Gordon potential (KGP) and Klein–Gordon field (KGF) equations for massive dyons from the generalized Proca–Maxwell equations. This formalism demonstrates that the octonionic KGP and KGF equations can be expressed in a single equation and it is equivalent to energy-momentum relation for dyons. As such, we have made an attempt to write the conservation of Noetherian current from the octonionic Klein–Gordon equations.     

Fisher information as the basis for Maxwell's equations

Maxwell's equations of classical electrodynamics may be derived on the following statistical basis. Consider a gedanken experiment whereby the mean space-time coordinate for photons in an electromagnetic field is to be determined by observation of one photon's space-time coordinate. An efficient (i.e. optimum) estimate obeys a condition of minimum Fisher information, or minimum precision, according to the second law of thermodynamics. The Fisher information I is a simple functional of the probability law governing space-time coordinates of the “particles” of the field. This probability law is modeled as the source-free Poynting energy flow density, i.e., the ordinary local intensity in the optical sense, or, the square of the four-vector potential. When the Fisher information is extremized subject to an additive constraint term in the total interaction energy, Maxwell's equations result.     

Kerr-Newman metric in deSitter background

In addition to the Kerr-Newman metric with cosmological constant several other metrics are presented giving Kerr-Newman type solutions of Einstein-Maxwell field equations in the background of deSitter universe. The electromagnetic field in all the solutions is assumed to be source-free. A new metric of what may be termed as an electrovac rotating de-Sitter space-time—a space-time devoid of matter but containing source-free electromagnetic field and a null fluid with twisting rays—has been presented. In the absence of the electromagnetic field, our solutions reduce to those discussed by Vaidya.     

A rotating homogeneous universe with an electromagnetic field

The field equations of general relativity are solved to describe a gravitational field due to a rotating homogeneous fluid in the presence of a Maxwellian source-free electromagnetic field. It turns out that the metric to describe this field is the well-known Robertson-Walker metric with positive space-time curvature or its particular case, the metric of the closed Einstein universe.     

Zur Hönl-Dehnenschen Formulierung des Machschen Prinzips

It is shown that the classification of curved space-times into Machian and antiMachian world models proposed byHönl andDehnen is inadequate. We prove that even the static Einstein model would be anti-Machian according to the definition of these authors, in contrast to their assertion. The proof is based on the theorem, established in this paper, that any Robertson-Walker space-time admits regular source-free Maxwell fields.     

THE PROBLEM OF MOTION IN THE KALUZA THEORY

It is shown that the equations of motion for a charged massive particle are consequences of the field equations in Kaluza unification theory of gravitation and electromagnetism, i.e., the equations of motion for the particle can be deduced from Kaluza field equations, just as that in Einstein's theory of motion of general relativity the equations of motion for a massive particle are consequences of the Einstein equations. Furthermore, the Lorentz equations for a particle maving in the Maxwell electromagnetic field on the Minkowskian space-time can also be obtained from the Maxwell equations by means of the Kaluze mechanism of the Maxwell theory.     

Kaluza理论的运动定律

本文指出,如同在广义相对论中粒子运动方程是场方程的推论一样,在引力场与电磁场的Kaluza统一理论中,粒子的运动方程也是场方程的一个推论,即带电粒子在引力场和电磁场中的运动方程可以从Kaluza统一理论中的场方程推导出来。本文进而在Minkowski时空的条件下,借助Maxwell理论的Kaluza形式,得到Maxwell方程也包含了带电粒子运动方程的结论。 关键词：     

Numerical simulation of Bessel beams by FDTD employing the superposition principle

Finite difference time domain (FDTD) method is adopted to build a Bessel beams simulation model according to homogeneousness and linearity of the Maxwell equations in source-free region. Validation for this model is confirmed by comparing the simulation results with the theoretical results solved with a vector Helmholtz equation in free space and good agreement with maximum error 2% has been demonstrated. It is indicated that FDTD could be an effective approach to analyze other complicated models of Bessel beams in source-free region by means of superposition principle.     

Symmetry mappings in Einstein-Maxwell space-times

General properties of Einstein-Maxwell spaces, with both null and nonnull source-free Maxwell fields, are examined when these space-times admit various kinds of symmetry mappings. These include Killing, homothetic and conformal vector fields, curvature and Ricci collineations, and mappings belonging to the family of contracted Ricci collineations. In particular, the behavior of the electromagnetic field tensor is examined under these symmetry mappings. Examples are given of such space-times which admit proper curvature and proper Ricci collineations. Examples are also given of such space-times in which the metric tensor admits homothetic and other motions, but in which the corresponding Lie derivatives of the electromagnetic Maxwell tensor are not just proportional to the Maxwell tensor.On leave from Mathematics Department, Monash University, Clayton, Victoria, 3168, Australia.     

Static conformally flat solutions in a general scalar-tensor theory of gravitation

Explicit field equations in the general scalar-tensor theory of gravitation proposed by Nordtvedt are obtained with the aid of a static spherically symmetric conformally flat metric. Exact static solutions of Nordtvedt-Barker field equations both in vacuum and in the presence of a source-free electromagnetic field are presented and studied. It is shown that there are no spherically symmetric static conformally flat solutions of Nordtvedt-Barker field equations representing perfect fluid distribution with disordered radiation obeying the equation of state=3p, except for the trivial empty flat space-time of Einstein's theory.     

Conditions for non-existence of static or stationary,Einstein–Maxwell,non-inheriting black-holes

We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein–Maxwell space–times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the symmetry of the space-time is not inherited by the electromagnetic field. We find that static degenerate black hole solutions are not possible and, subject to stronger assumptions, nor are static, non-degenerate or stationary black holes. We describe the possibilities if the stronger assumptions are relaxed.     

Stationary axially symmetric Brans-Dicke-Maxwell fields

A method is presented which enables one to obtain solutions to the stationary axially symmetric Brans-Dicke fields coupled to source-free Maxwell fields from the solutions of the Einstein-Maxwell equations in Einstein's theory. The Brans-Dicke analog of the Kerr-Newman solution has been obtained as an example.     

Electrodynamics of a continuous medium in a system with specified structure

It is shown that electrodynamics can be considered not only in Minkowski space but also in Riemannian space-time. The exact solutions for the electric field within and beyond a charged plate and a sphere and the space-time geometry are found without applying the Einstein equations. The space-time geometry of a Born-rigid noninertial frame of reference (NFR) with global linear acceleration in space-time having constant curvature is obtained on the basis of the structural equations (integrability conditions). A new Lorentz-covariant condition of stationarity for possible solutions to the Maxwell equations for the particles frozen in a Born-rigid NFR is formulated. In an inertial frame of reference this condition is equivalent to zero four-curl of the field of four-accelerations of particles. This condition provides zero relativistic generalized radiation friction force. The propagation of electromagnetic waves in this NFR and the Doppler effect are described. The limitations imposed on the energy-momentum tensor in the Einstein equations are derived.