Space-time Curvature of Classical Electromagnetism

We begin with the time-dependent electric and magnetic dipole solution of Maxwell's equations in Minkowski space. This Maxwell field is then used to determine the behavior of the gravitational field (the Weyl tensor) as a second-order perturbation off of the Minkowski background. From the Weyl tensor we go on and find the spin-coefficients and the full metric in this approximation. The physical meaning of many of the relations is discussed. In particular we can identify the c...

Gravity field theory and electromagnetic field theory are well established and confirmed by experiments. The Schwarzschild metric and Kerr Metric of Einstein field equation shows that the spatial differential of time gauge is the gravity field. For pure time displacement field, when its spatial differentials are commutative, conservative fields can be established. When its spatial differentials are non-commutative, Maxwell electromagnetic field equations can be established. W...

Principles of Maxwell, Lorentz, Milne, Dirac and Feynman are combined to unify gravity with electromagnetism.

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to fo...

It is shown that unification of gravity and electromagnetism can be achieved using an affine non-symmetric connection $\Gamma^\lambda_{\mu\nu} \neq \Gamma^\lambda_{\nu\mu}$ and $\Gamma_\mu = \Gamma^\lambda_{[\mu\lambda]}\neq 0$. $\Gamma_\mu$ is shown to be the source of the electromagnetic field. This unification is based on {\em projective invariance} which is broken by matter fields, opening up the possibility of a unified theory of all forces in which gravity emerges as a ...

We show that the problem of unifying electromagnetism with gravity has an elegant solution in classical physics through the phenomenon of induction. By studying the way that induction leads to the formation of electromagnetic fields, we identify the classical field equations which the unified field must satisfy and a corresponding set of constitutive equations for the medium sustaining the field. The unification problem is then reduced to the problem of finding the exact form...

We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang-Mills theories, and achieve a metr...

The effect of gravity in Maxwell's equations is often treated as a medium property. The commonly used formulation is based on managing Maxwell's equations in exactly the same form as in Minkowski spacetime and expressing the effect of gravity as a set of constitutive relations. We show that such a set of Maxwell's equations is, in fact, a combination of the electric and magnetic fields defined in two different non-covariant ways, both of which fail to identify the associated ...

After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotatio...

We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve these paradoxes with a single postulate, namely, the preservation of the local properties of time. This postulate forces the introduction of four additional degrees of freedom into the space-time structure whose transformation properties are...