On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy

Abstract

AbstractIn this paper the independent equations of continuum electrodynamics and their quantity are investigated, beginning with the standard equations used in special and general relativity. Using differential identities it is checked that there are as many independent equations as there are unknowns, for the case with given sources as well as for the general case where the motion of the charged medium producing the field is unknown. This problem is then discussed in an alternative theory of gravity with a preferred reference frame, in order to constrain an additional, “interaction” energy tensor that has to be postulated in this theory, and that would be present also outside usual matter. In order that the interaction tensor be Lorentz-invariant in special relativity, it has to depend only on a scalar fieldp. Since the system of electrodynamics is closed in the absence of the interaction tensor, just one scalar equation more is needed to close it again in the presence ofp. That equation is taken to be the equation for charge conservation. Finally, the equations that allow the determination of fieldpare derived in a given weak gravitational field and in a given electromagnetic field.