Related papers: From Maxwell Stresses to Nonlinear Field Equations
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
We show that the linearized equations of the incompressible elastic medium admit a `Maxwell form' in which the shear component of the stress vector plays the role of the electric field, and the vorticity plays the role of the magnetic…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…
Suggested modification of the Einstein-Maxwell system, such that Maxwell equations become non-gauge and nonlinear. The theory is based on assumption that observable (i.e., felt by particles) metric is $ {\tilde{g}}_{ab} = g_{ab} -…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…
We consider quantum gravitational corrections to Maxwell's equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the…
A mathematical proof is given that Maxwell's equations are an {\it artifact} of Hodge theory together with the laws of Gauss and Amp\`ere, taken as axioms. They are thus geometric in nature, independent of any specific physical mechanisms,…
The nonlocal electrodynamics of accelerated systems is discussed in connection with the development of Lorentz-invariant nonlocal field equations. Nonlocal Maxwell's equations are presented explicitly for certain linearly accelerated…
By introducing external Maxwell and gravitational fields we modify the Bonnor--Vaidya field of an arbitrarily accelerating charged mass moving rectilinearly in order to satisfy the vacuum Einstein--Maxwell field equations approximately,…
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time,…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
Non-linear nature of Einstein equation introduces genuine relativistic higher order corrections to the usual Newtonian fluid equations describing the evolution of cosmological perturbations. We study the effect of such novel non-linearities…