On Charge Conservation in a Gravitational Field

Abstract

According to the “gravitationally-modified” Maxwell equations that were proposed for an alternative scalar theory with an “ether”, electric charge would not be conserved in time-dependent gravitational field. We define an asymptotic expansion scheme for the electromagnetic field in a weak gravitational field. This allows us to assess the amounts of charge production or destruction which are thus predicted. These amounts seem high enough to discard that version of the gravitationally-modified Maxwell equations. We show that this failure is due to the former assumption of additivity of the energy tensors: an “interaction energy tensor” has to be added. Then the standard Maxwell equations in a curved spacetime become compatible with that scalar theory, and they predict charge conservation.