We review a technique for solving a class of classical linear partial differential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar Laplacian
and a complexified Hertz potential. The complexification prescription ensures the existence of regular physical solutions with chirality and propagating, non-singular, pulse-like characteristics that are bounded in all three spatial dimensions. The technique is applied to the source-free Maxwell, Bopp-Lande-Podolsky and linearised Einstein field systems, and particular solutions are used for constructing classical models describing single-cycle laser pulses and a mechanism is discussed for initiating astrophysical jets. Our article concludes with a brief introduction to spacetime Clifford algebra ideals that we use to represent spinor fields. We employ these to demonstrate how the same technique used for tensor fields enables one to construct new propagating, chiral, non-singular, pulse-like spinor solutions to the massless Dirac equation in Minkowski spacetime.
This paper invokes a new mechanism for reducing a coupled system of fields (including Einsteins equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current observational
astronomy. Our approach is formulated as a classical Einstein-vector-scalar-Maxwell-fluid field theory on a spacetime with three-sphere spatial sections. Analytic cosmological solutions are found using local charts familiar from standard LFRW cosmological models. These solutions can be used to describe different types of evolution for the metric scale factor, the Hubble, jerk and de-acceleration functions, the scalar spacetime curvature and the Kretschmann invariant. The cosmological sector of the theory accommodates a particular single big-bang scenario followed by an eternal exponential acceleration of the scale factor. Such a solution does not require an externally prescribed fluid equation of state and leads to a number of new predictions including a current value of the jerk parameter, Hopfian-like source-free Maxwell field configurations with magnetic helicity and distributional bi-polar solutions exhibiting a new charge conjugation symmetry. An approximate scheme for field perturbations about this particular cosmology is explored and its consequences for a thermalisation process and a thermal history are derived, leading to a prediction of the time interval between the big-bang and the decoupling era. Finally it is shown that field couplings exist where both vector and scalar localised linearised perturbations exhibit dispersive wave-packet behaviours. The scalar perturbation may also give rise to Yukawa solutions associated with a massive Klein-Gordon particle. It is argued that the vector and scalar fields may offer candidates for dark-energy and dark-matter respectively.
It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation for pertur
bations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. These solutions are classified in terms of their chirality and generate a family of non-stationary spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.
This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly v
arying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.
Electromagnetic Casimir stresses are of relevance to many technologies based on mesoscopic devices such as MEMS embedded in dielectric media, Casimir induced friction in nano-machinery, micro-fluidics and molecular electronics. Computation of such st
resses based on cavity QED generally require numerical analysis based on a regularization process. A new scheme is described that has the potential for wide applicability to systems involving realistic inhomogeneous media. From a knowledge of the spectrum of the stationary modes of the electromagnetic field the scheme is illustrated by estimating numerically the Casimir stress on opposite faces of a pair of perfectly conducting planes separated by a vacuum and the change in this result when the region between the plates is filled with an incompressible inhomogeneous non-dispersive dielectric.
A new mathematical and computational technique for calculating quantum vacuum expectation values of energy and momentum densities associated with electromagnetic fields in bounded domains containing inhomogeneous media is discussed. This technique is
illustrated by calculating the mode contributions to the difference in the vacuum force expectation between opposite ends of an inhomogeneous dielectric non-dispersive medium confined to a perfectly conducting rigid box.
Applications of the covariant theory of drive-forms are considered for a class of perfectly insulating media. The distinction between the notions of classical photons in homogeneous bounded and unbounded stationary media and in stationary unbounded m
agneto-electric media is pointed out in the context of the Abraham, Minkowski and symmetrized Minkowski electromagnetic stress-energy-momentum tensors. Such notions have led to intense debate about the role of these (and other) tensors in describing electromagnetic interactions in moving media. In order to address some of these issues for material subject to the Minkowski constitutive relations, the propagation of harmonic waves through homogeneous and inhomogeneous, isotropic plane-faced slabs at rest is first considered. To motivate the subsequent analysis on accelerating media two classes of electromagnetic modes that solve Maxwells equations for uniformly rotating homogeneous polarizable media are enumerated. Finally it is shown that, under the influence of an incident monochromatic, circularly polarized, plane electromagnetic wave, the Abraham and symmetrized Minkowski tensors induce different time-averaged torques on a uniformly rotating materially inhomogeneous dielectric cylinder. We suggest that this observation may offer new avenues to explore experimentally the covariant electrodynamics of more general accelerating media.
