On the Einstein-Maxwell field equations

Abstract

Starting with the Einstein-Maxwell field equations in general relativity we construct the general differential equations governing the components of the metric tensor. We do this in a fashion completely analogous to that which we follow in Einstein-Infeld-Hoffmann and Einstein-Infeld theory. These equations allow us to findhif in various orders. An answer to our problem up to the first relativistic corrections is a computational work to find4h00, since the other terms2h00,2hαβ and3h0α are as in a pure gravitational case. On the other hand, using the defined Einstein-Maxwell tensor, we give the equations of motion of two charged particles in the 0th order; also, the generalization is given in the case ofn particles.