84 v 1 1 8 M ay 2 00 0 What is general relativity silent on ?

Gravitational field in general relativity is a manifestation of spacetime curvature and (unlike the electromagnetic field) is not a force field. A body falling toward the Earth is represented by a geodesic worldline which means that no force is acting on it. If a body is on the Earth’s surface, 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. This paper pursues two aims to bring forward that question and to outline an approach toward resolving it which was initiated by Fermi in 1921. General relativity provides a consistent no-force explanation of gravitational interaction of bodies following geodesic paths. However, it is silent on the nature of the force acting upon a body deviated from its geodesic path. Here we shall show that a corollary of general relativity that the propagation of electromagnetic signals (for short light) in a gravitational field is anisotropic in conjunction with the classical electromagnetic mass theory [1]-[6] sheds some light on the nature of that force in the case of charged particles. Consider a classical [7] electron at rest in the non-inertial reference frame N of an observer supported in the Earth’s gravitational field. Following Lorentz [4] and Abraham [5] we assume that the electron charge is uniformly distributed on a spherical shell. The repulsion of the charge elements of an electron in uniform motion in flat spacetime cancels out exactly and there is no net force acting on the electron. As we shall see bellow, however, the anisotropic velocity of light in N (i) gives rise to a self-force acting on an electron deviated from its geodesic path by disturbing the balance of the mutual repulsion of its charge elements, and (ii) makes a free electron fall in N with an acceleration g in order to balance the repulsion of its charge elements. No force is acting upon a falling electron (whose worldline is geodesic) but if it is prevented from falling (i.e. deviated from its geodesic path) the mutual repulsion of the elements of its charge becomes unbalanced which results in a self-force trying to force the electron to fall. This force turns out to be precisely equal to the gravitational force F = mg, where m = U/c represents the passive gravitational mass of the electron and U is the energy of its field. In 1921 Fermi [8] studied the nature of the force acting on a charge at rest in a gravitational field of strength g in the framework of the classical electromagnetic mass theory. The potential