Space-time Curvature of Classical Electromagnetism

The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of electromagnetism the general laws are expressed as geometric (coordinate-free) relations between quantities on a four-dimensional spacetime manifold. Based on these laws, and exterior calculus on metric spaces, we derive fields and relations th...

A theory which achieves a complete geometrical unification of gravitation and electromagnetism (GUGE) is presented. This new theory is based on a recent proposal of proper time redefinition that leads to the construction of a Riemann metric, which naturally unifies gravity and electromagnetism. The 5--dimensional Riemann metric which arises looks exactly the same as the one postulated in the Kaluza-Klein (KK) 5-dimensional theory. Nevertheless, there are deep differences betw...

It is possible to describe a universal scalar field of time but not a universal coordinate of time and to attribute its non-geodesic alignment to the electromagnetic phenomena. A very surprising outcome is that not only mass generates gravity, but also electric charge does. Charge is, however, coupled to a non-geodesic vector field and thus is not totally equivalent to inertial mass. Only the entire "Energy-Momentum" tensor has a vanishing divergence. The model can be seen as...

Einstein's unified field theory is extended by the addition of matter terms in the form of a symmetric energy tensor and of two conserved currents. From the field equations and from the conservation identities emerges the picture of a gravoelectrodynamics in a dynamically polarizable Riemannian continuum. Through an approximate calculation exploiting this dynamical polarizability it is argued that ordinary electromagnetism may be contained in the theory.

We present a five dimensional unified theory of gravity and electromagnetism which leads to modified Maxwell equations, suggesting a new origin for galactic magnetic fields. It is shown that a region with nonzero scalar curvature would amplify the magnetic fields under certain conditions.

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically charged from neutral matter. Electric charge and magnetic flux are postulated to be conserved. As a consequence, the inhomogeneous and the homogeneous Maxwell equations emerge expressed in terms of the excitation H and the field strength F, res...

We consider the evolution of electromagnetic fields in curved spacetimes and calculate the exact wave equations of the associated electric and magnetic components. Our analysis is fully covariant, applies to a general spacetime and isolates all the sources that affect the propagation of these waves. Among others, we explicitly show how the different parts of the gravitational field act as driving sources of electromagnetic disturbances. When applied to perturbed FRW cosmologi...

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting wit...

The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the electromagnetic field in multi-dimensional pseudo-Euclidean (flat) spaces has also been developed and investigated. Based on the two arising first-class constraints we have generalized to multi-dimensional spaces a number of different gaug...

A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way to a better understanding of the structure of the energy-momentum tensor in the Einstein Field Equations. Hence it is directly relevant to problems in modern cosmology. The derivation, independent of the perturbation theory of Einstein's...