Equations of Motion without Infinite Self-Action Terms in General Relativity

The role of the Bianchi identity in obtaining the equations of motion in general relativity is further discussed in connection with the problem of the infinite self-action terms. It is shown that because of this identity and under certain assumptions (concerning the type of singularity of the Christoffel symbols near the particle), there is a possibility of obtaining an equation of motion, free of infinite self-action terms, without referring to any renormalization procedure. This is the Infeld equation of motion which describes the motion of a particle of finite mass and in which the time coordinate is taken to be the independent parameter. Besides that, however, the Bianchi identity imposes certain constraints that the field functions have to satisfy in addition to the equation of motion.