A Classical Complete Action for a System of Small-Point Massive Charged Particles in General Relativity

Abstract

A classical action which describes the motion of a system of small-point massive charged particles including the existence of the electromagnetic and gravitational self-forces, Maxwell equations and Einstein field equations is presented. The action possesses the particularity of being a functional of the variables z i ( τ i ), the trajectory of the i -particle, A α ( x ), the electromagnetic 4-potential, and g αβ ( x ), the metric tensor. It is also considered that the metric tensor g αβ ( x ) and the potential A α ( x ) are not functions of the trajectory of each particle when the variations with respect to the trajectories of the particles are done. That is, the action is complete. The electromagnetic and the gravitational self-forces are analyzed.