On the nature of the force acting on a charged classical particle deviated from its geodesic path in a gravitational field

Vesselin Petkov

Published 2000-05-18, updated 2001-10-24Version 5

In general relativity the gravitational field is a manifestation of spacetime curvature and unlike the electromagnetic field is not a force field. A particle falling in a gravitational field is represented by a geodesic worldline which means that no force is acting on it. If the particle is at rest in a gravitational field, however, its worldline is no longer geodesic and it is subjected to a force. The nature of that force is an open question in general relativity. The aim of this paper is to outline an approach toward resolving it in the case of classical charged particles which was initiated by Fermi in 1921.