Paths of charges in general relativity as geodesics of Einstein's non-Riemannian geometry

Abstract

The equation of motion of charged incoherent matter, and hence of a test charge, in general relativity can be written as the geodesic equation of an affine connection. Here, the connection is chosen to satisfy a condition which has the form of one of the basic geometrical principles of Einstein's unified field theory. The symmetric part of the fundamental tensor of the geometry is chosen to be the metric tensor of general relativity; equations to be satisfied by the skew part, involving the electromagnetic field, are obtained. An alternative condition on the affinity is also considered.