The Geometrization of Maxwell’s Equations and the Emergence of Gravity

A recently proposed classical field theory in which Maxwell’s equations are replaced by an equation that couples the Maxwell tensor to the Riemann-Christoffel curvature tensor in a fundamentally new way is reviewed and extended. This proposed geometrization of the Maxwell tensor provides a succinct framework for the classical Maxwell equations which are left intact as a derivable consequence. Beyond providing a basis for the classical Maxwell equations, the coupling of the Riemann-Christoffel curvature tensor to the Maxwell tensor leads to the emergence of gravity, with all solutions of the proposed theory also being solutions of Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and/or dark energy. Both electromagnetic and gravitational phenomena are put an equal footing with both being tied to the curvature of space-time. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena as well as the consistency of solutions with those of the classical Maxwell and Einstein field equations is emphasized throughout. Unique to the proposed theory and based on specific solutions are the emergence of antimatter and its behavior in gravitational fields, the emergence of dark matter and dark energy mimicking terms in the context of General Relativity, an underlying relationship between electromagnetic and gravitational radiation, and the impossibility of negative mass solutions that would generate repulsive gravitational fields or antigravity. Finally, a method for quantizing the charge, mass, and angular momentum of particle-like solutions as well as the possibility of superluminal transport of specific curvature related quantities is conjectured.

Electromagnetic Superpotentials forthe Liénard - Wiechert Field

Weert deduced a superpotential for the bounded part of the Maxwell tensor \(T_{ab}\) $ associated to the Liénard-Wiechert field. In this work we explicitly construct the non-local superpotential for the radiative part of \(T_{ab}\).

Numerical Analysis of Electrokinetic Interaction Between a Colloidal Particle and a Planar Wall

At present electrokinetics is widely used in biotechnology for the manipulation of biomolecules, such as separation of proteins, sequencing of polypeptide chains etc. Thus it is important to study the interaction forces between the molecules and the surfaces they come in contact. In the present study we numerically solve Poisson-Nernst-Planck (PNP) model to obtain electric double layer (EDL) and its interaction when a cylindrical particle is in proximity of a planar charged wall. The axial flow field induced by the external electric field applied parallel to the planar wall is obtained from the solution of Stokes equations. The electrophoretic motion of the particle is then obtained by balancing the forces acting on the particle such as hydrodynamic, electrostatic etc. The EDL interaction force calculated using Maxwell tensor in conjunction with PNP model is validated by comparing with the one obtained from surface-element-integration method.