A representation of the electromagnetic field in the presence of curvature

Classical treatments of electromagnetism in the presence of a gravitational field generally consist of embedding Maxwell's equations into the metrical continuum by writing them in a covariant form. Except for the coupling thr ough the energy-momentum tensor, this treatment gives the electromagnetic f ield equations an existence that is distinct from and independent of that o f the gravitational field equations of general relativity. Here an alternat ive formulation is presented in which electromagnetic fields along with the ir sources are described in terms of the metric tensor g(mu nu) and a conti nuous four-component vector field u(lambda). In the presence of ponderable mass, the continuous four-component vector field u(lambda) is interpreted a s the ordinary 4-velocity describing the mass's motion. Because the propose d equations describing the electromagnetic field differ from the classical Maxwell equations, their ability to describe classical physics is shown by direct calculation. This is done using Einstein's classical gravitational f ield equations along with an energy momentum tensor constructed using the p roposed electromagnetic field equations. As an example, the asymptotic beha vior of the presented equations is investigated under the restriction of ax ial symmetry. In this case, the equations lead naturally to the expected as ymptotic descriptions of the gravitational and electromagnetic fields of a point charge superimposed on a magnetic dipole. Finally, the description of an electromagnetic plane wave in terms of the dynamical variables (g(mu nu ), u(lambda)) in the weak field limit is presented.