Abstract

Newtonian and Machian aspects of the stationary gravitational field are brought into formal analogy with a stationary electromagnetic field. The electromagnetic vector potential equals (up to a factor) the timelike Killing vector field. The current density is given by the contraction of the Killing vector with the Ricci tensor. A coordinate-dependent split in electric and magnetic field vectors is given, and some results of classical electrodynamics are used to illustrate the analogy. In the linearized theory, the usual Maxwell equations are obtained. The analogy also holds from the point of view of particle motion. The geodesic equation is brought into a special form that exhibits an analog to the Lorentz force. Two examples (which have played an important role in the theoretical discovery of Machian effects) are considered