Dyonic Field Equations in Arbitrary Media

Starting with the generalized Maxwell field equation of dyon, the matrix form of generalized Maxwell field equation is formulated in a compact manner. The Maxwell field equations and Lorentz force for dyon in term of the matrix are also derived in arbitrary media (material media). It represents an additional field, which shows polarization and magnetization for the electric and magnetic charge. Finally, the Continuity equation for dyon is also derived.

Dyonic Field Equations in Arbitrary Media

Starting with the generalized Maxwell field equation of dyon, the matrix form of generalized Maxwell field equation is formulated in a compact manner. The Maxwell field equations and Lorentz force for dyon in term of the matrix are also derived in arbitrary media (material media). It represents an additional field, which shows polarization and magnetization for the electric and magnetic charge. Finally, the Continuity equation for dyon is also derived.

Electromagnetic effects on the inhomogeneity of planar symmetry

In this work, we aim to identify the effects of electromagnetic field on the energy density inhomogeneity in self-gravitating plane symmetric spacetime filled with imperfect matter in terms of dissipation and anisotropic pressure. We formulate the Einstein–Maxwell field equation, conservation laws, evolution equations for the Weyl tensor and the transport equation for diffusion approximation. Inhomogeneity factors are identified for some particular cases of non-dissipative and dissipative fluids. For non-dissipative case, we analyze the inhomogeneity factor for dust, isotropic and anisotropic matter distributions while dissipative matter distribution includes the inhomogeneity factor only for geodesic dust fluid. We conclude that electric charge increases the inhomogeneity in the energy density which is due to shear, anisotropy and dissipation.

CONSERVED CURRENT FOR GENERAL TELEPARALLEL MODELS

The obstruction for the existence of an energy-momentum tensor for the gravitational field in GR is connected with vanishing of first order invariants in (pseudo) Riemannian geometry. This specific geometric property is not valid in alternative geometrical structures1,2. A parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields ϑa is considered. A general 3-parameter class of global Lorentz invariant teleparallel models is considered. It includes a 1-parameter subclass of models with the Schwarzschild coframe solution (generalized teleparallel equivalent of gravity) 3. By introducing the notion of a 3-parameter conjugate field strength F linear in the strength Ca = dϑa the coframe Lagrangian is rewritten in the Maxwell-Yang-Mills form L = 1/2Fa ∧ Ca. The field equation turns out to have a form d * Fa = Ta completely similar to the Maxwell field equation. By applying the Noether procedure, the source 3-form Ta is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source Ta of the coframe field is interpreted as the total conserved energy-momentum current of the coframe field and matter4. The energy-momentum tensor is defined as a map of the module of current 3-forms into the module of vector fields 5. Thus an energy-momentum tensor for the coframe is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in the standard GR. The result is: The standard GR has a neighborhood of viable models with the same Schwarzschild solutions. These models however have a better Lagrangian behavior and produce an invariant energy-momentum tensor.